Tsuga-Ike Highlands is quite close from Tokyo, and there are night buses at reasonable prices (if you can sleep in buses).
Gala Yuzawa is a fairly large ski resort the can be reached by the bullet train in less than two hours from Tokyo. Echigo Yuzawa, a town close by, has many small ski resorts. Both places have lots of hotels to stay, at good rates.
Saku Daira ski resort offers good deals for bullet train travelers. There is a ticket that covers the two way train ride, skiwear and equipment, and also the bus ride from the station.
Hokkaido offers much better snow (powder snow0 and larger resorts, if you are not visiting Tokyo.