Read the previous article on Tips for road trips. Everything that applies to fair weather, applies even more so to inclement weather.
Consider taking an advanced drivers education course, especially if you have no/little experience driving on snow or never learned how to recover from a skid or similar conditions.
GPS navigation units (Garmin, Magellan, TomTom, etc.) for road travel have become so inexpensive lately, anyone doing winter driving beyond their home area should use one. Be sure it contains maps of all relevant countries if you cross international borders, and don't wait until the last minute to figure out how your unit works. Ideally, you should have at least a month of experience in your home area before going on a long winter road trip. (Even when you know how to get to familiar, nearby locations, practice using your GPS anyway.) Be certain any hand-held unit is suitable for navigation while driving with spoken turn-by-turn promps. A GPS device intended for just hiking, boating, and the like is NOT suitable while driving. Remember: One wrong turn onto a winter-abandoned road can be fatal.
Warm clothing (including ski caps, gloves, and rubber boots that fit over shoes) and blankets (or sleeping bags). If you live in a mild climate and can't find such items where you normally shop, try a sporting goods store. In larger cities there are outdoor sports shops that carry all year round clothes to wear in very cold conditions. If you are planning to drive in climate with very low temperatures, make sure to keep extra outdoor clothing in the passenger compartment, not in the trunk. This will keep the clothes warm at all time, saving you from having to put on cold clothing when already cold, should you have problems with your vehicle.
Extra non-perishable ready-to-eat food
First aid kit
Extra prescription medication (if applicable), especially medication that can mean the difference between life and death in the short term, such as insulin for diabetes, inhalers/EpiPen for asthma/anaphylactic shock, and (cortico)steroid treatments. Also, drugs which may produce uncomfortable and/or life-threatening withdrawals such as tranquilizers (esp. benzodiazepines), narcotic pain medication, antidepressants, anticonvulsants, and certain blood pressure medication should be with physically dependent individuals at all times.
Lighter and strike-anywhere matches
Portable radio with AM band and batteries, even if your vehicle has one.
Flashlight (torch) with batteries
Ice scraper with a brush.
A lightweight snow shovel (or any shovel, if your can't buy a snow shovel locally)
Sun glasses -- on a sunny, winter day, the glare on the road from snow (or even water) can be quite bad
Don't forget your cell phone and its in-vehicle charger. However, service may not be available in rural areas. If you're planning to upgrade or replace your cell phone, look for a model that includes GPS (many do). Except for some large-screen models (like the i-phone), these are not useful for navagation at all; only for locating someone.
Spare vehicle key to carry on your person
Bucket of sand in case your vehicle gets stuck (especially without all-wheel drive)
Tire chains or cables (see below)
Last, but not least, spare batteries for all the above battery-operated equipment.
If using a GPS device, mapping software or websites to plan your route, always double-check it yourself against a detailed, printed map or atlas (e.g. Rand McNally, AAA/CAA, Michelin, etc.) Always select "fastest" (never "shortest") route, as this will help keep it to the main highways. Of course, you shouldn't drive faster than conditions permit. Warning: Selecting "shortest route" or otherwise taking short cuts in wintertime could easily get you stranded, and can be deadly!
Avoid anything below a state/provincial route except for the last few miles/kilometers to your destination, where necessary. On some minor roads, there might not be another vehicle for days, weeks, or even months. Software maps are not as good as paper maps in showing how "minor" a less-used road is. Some aren't even paved, but look as good on a computer screen or GPS device as a well-paved, busy thoroughfare. That said, maps published by the Government may have all state/provincial routes printed with equally bold lines, regardless of how well maintained and frequently traveled they are. Commerically-produced maps are often much better at discerning major highways from minor ones.
If at all possible, allow for a couple days of flexibility so you can wait out a winter storm (preferably before leaving home). This is especially important for those who have little winter driving experience. Check the forecast before departing and try to avoid the worst of it. The most popular sites online are weather.com and wunderground.com.
Check highway conditions for all roads you will be traveling at the state/provincial highway department's website (search on Google, Yahoo, etc.). In the USA, include the word "state" (i.e. "Montana state") in your search. Be especially careful with routes that take you through mountains or any terrain having steep or long grades.
Always get advice from locals beforehand about conditions off the main highways. The best route may not be obvious to you, or even be shown on a paper map. Also, let them know when you plan to arrive, with updates on any delays.
A four-wheel-drive vehicle is preferable to a two wheel drive.
If 4x4 vehicles are unavailable, a vehicle with a limited slip differential and/or traction control is highly recommended for driving on snow and ice. Two-wheel-drive vehicles without such a device can very quickly get stuck. In this situation, one wheel will block (have no power), while the other spins freely, unable to move the vehicle from this spot. An ordinary differential (most vehicles) provides equal power to the left and right wheels. Thus, if one wheel is on ice or buried in snow, it takes almost no power for this wheel to spin, while the other wheel receives likewise, but needs a whole lot more.
Front-wheel-drive is preferable to rear-wheel-drive (most Mercedes and BMW). Also, most smaller and mid-sized cars have front-wheel-drive nowadays.
A small, lightweight 4x4 vehicle with good ground clearance is preferable to a SUV or off-roader, especially on mountain roads. Narrow tires perform better on snow than wide tires. Heavy vehicles are more likely to slip on steep roads, and are also more difficult to rescue by pushing.
The same rule applies to two-wheel-drive vehicles: A subcompact is better for snowy conditions than a mid-size or luxury car.
Almost all cars manufactured in the past few years for Europe or Japan have ABS, but NOT the USA and Canada, many cheaper vehicles in USA or Canada do NOT have ABS at all (as of 2010). US Department of Transport has planned to make it mandatory, but the plan has not completely phase in yet.
100% electric cars (no combustion engine) are not suitable for long-distance winter driving due to the batteries not functioning as well in cold weather. Thus, what may have been within range during warmer weather, can easily be out of range when it's freezing. In addition, any heating inside the car comes directly from the battery, lowering its range even further. (Combustion engines produce a lot of excess heat, which either goes to the radiator, or is used to heat the inside of the vehicle.) If the battery of an electric car loses its charge, towing might be the only option, followed by hours of waiting while it recharges. None of this applies to hybrids (e.g. Toyota Prius), though don't expect the fuel economy to be quite as good.
Check anti-freeze (coolant) levels, and have it changed every two to four years (depending on type used).
Make sure brakes and ABS system are in good condition.
Check heater and defroster and make sure they heat with no smell.
Check condition of the tires and their pressure. Don't forget the spare tire and jack.
Check that the tires (if not relying on chains/cables) are proper winter tires, and not just "all-weather" tires. Although these satisfty the legal requirements in some countries, they leave much to be desired for.
A vehicle's battery can't work as well in cold weather. Have it replaced if it's near or over the pro-rated warranty period. On an older vehicle, check the belts, and an alternator test is also a good idea. Fill an older, unsealed battery with distilled water (but don't overfill).
Replace worn wiper blades and top off washer fluid. Don't use plain water as it will freeze. On the other hand, antifreeze intended for the radiator may damage your vehicle's paint. Look for the winter-type washer fluid at auto parts stores which has a freezing point of about -20F/-30C. Even though it's on the other side of the windshield, using the defroster also helps prevent the washer fluid from freezing.
Studded snow tires are good for winter driving conditions, though a few U.S. states prohibit them (except, perhaps, for out-of-state vehicles just passing through). On the other hand, in Sweden it's illegal to drive without proper winter tires in the winter, they don't have to be studded though. The tread depth must be at least 6/32" or 5 mm (or whatever local law requires), which is several times deeper than for regular tires wearing out. If you live in an area where it doesn't normally snow, it's probably not worth the time and expense.
Especially without snow tires, always bring tire chains or cable chains. Tire chains give better traction, but are more difficult to install and remove. Know your tire size (e.g. P195/60R-15) before purchasing. When needed, install on the drive wheels (i.e. front for front-wheel-drive, rear for rear-wheel-drive). If unsure about drive wheels, every rear-wheel-drive vehicle has a black sphere-shaped thing (the differential) on its rear axle between the tires. Note that 4WD/All-WD vehicles will have one there also. For 4WD/All-WD usually the front is best, but check owner's manual. Only use chains in snow or icy conditions, and remove them as soon as they're no longer needed. Don't even try them on for size on a hard, bare surface such as concrete. They might spin out and damage the chains, concrete, and/or wheel well of the vehicle, and possibly injure someone.
Driving on snow, and especially ice, requires extra stopping distance. Use extreme caution when going downhill.
You cannot drive at highway/freeway speeds with chains on.
Keep your fuel tank at least half full at all times.
For vehicles with ABS anti-locking brakes, do not pump the brake pedal if you start to skid.
If you miss your freeway exit, get off at the next one and turn around. Continuing on to a less-used alternate route in winter is foolish.
If a mountain pass is closed due to the weather, there's a good reason for it. Don't even think of using local roads to get around the closure. Saving a day or two is not worth risking your life.
In blizzard/white-out conditions, you may not be able to see anything through the windshield. Try rolling down the window and sticking your head outside. Then, find a safe place to get off the road and stay there until conditions improve.
Ice is more likely to form on bridges. Slow down when going over them, especially on the motorway.
When driving downhill, no amount of technical gadgetry (ABS,4x4,ESP,...) will protect you against skidding. Snow chains are the only remedy.
Keep in mind that even though a 4x4 is great for providing forward traction, it will not improve stopping distance.
Skidding (sideways) is most likely to start with the driving wheels. I.e., on a car with front wheel drive a front wheel skid is most likely, rear wheel skid on a rear wheel drive, and on a 4x4 don't be surprised if all four wheels loose the grip at the same time!
Stay in your vehicle. It can provide enough shelter to save your life. Also, it's much easier for rescuers to see.
Run the engine for only 5-10 minutes each hour, with the heater on to the max. Make sure drifting snow doesn't block the exhaust pipe. Check each time before restarting engine (unless obvious not snowing/no wind), and shovel any snow out from the rear end as needed.
Protect any critical liquid medications such as insulin from becoming frozen. If there is no more heat from your vehicle, keep it next to your body.
If you must go outside to search for help or food, do so only in the morning hours after sunrise when it's not snowing or foggy, and then only for one hour each way. If for some reason, you've left your vehicle and can't return, make or dig a snow shelter (i.e. primitive igloo) at once.
Assuming no cell phone service, have your phone on every 15 minutes per hour. Then turn it totally off (usually the "end" button on newer phones) to help save its battery. Don't waste the battery trying to dial numbers where there's no service. Rescuers can use portable receivers and direction finders to pick up its signal. However, even if they do, it's not possible to communicate with you over the phone. If battery power has become critical, leave the phone off after dark, as rescue efforts are often suspended sunset to sunrise.