Catch a shinkansen from Tokyo station to Urasa (浦佐) in Niigata. It's one of the snowiest places there. The trains leave hourly, cost is ¥8200 each way, takes about 90 minutes, so this could easily be a day trip. No need even for a reservation--go to Tokyo station, buy a ticket, get on the next train. In Urasa, catch a local bus or have a taxi take you from the station to one of the 6-8 ski areas there.
Urasa is guaranteed to have snow in January. I was there once in March and the snow was 3-4 meters deep.