The busiest crossing of the Oslofjord runs east to Moss every half hour. 30 minutes, NOK 28.
Even though the Vestfold Line does not pass through the Horten city proper, Skoppum station is inside the Horten municipality, and buses into Horten are often available. Another option is to use the station at Holmestrand.
Trains run about hourly, with more trains during the Monday-Friday morning and evening peak, and fewer on Saturdays and Sundays.
Most of Horten is within walking distance.