Are you planning on living there for the winter? Or do you just mean for the weekends?
Day trips from Tokyo can be super cheap if you speak Japanese (or have someone that can do it for you). There are bus tours leaving Shinjuku and Ikebukuro that will do return bustrip, and lift pass (sometimes even rentals, but the stuff they provide for rentals is from the 80s), for around 5000-8000yen.
There are two options; leave at night (10-11pm) and the bus will take a very slow road to the mountains getting you there at around 5-6am. You then have a few hours to rest/get changed before catching the first lifts out. The second option is the morning bus which leaves at around 7am, getting you to the mountain around 10-11:30. Its a bit later, so my tactic for those days is to bring some onigiri to eat on the lifts and then just board the entire time until you need to go back to catch the bus at 5pm. Both options will get you back to Tokyo around 10pm.
My wife and i will do this pretty much every weekend during winter. Its cheaper than a night out and the schedule usually means you dont have time to go out drinking that weekend anyway.
There are also bus/accommodation tours, that will do the same schedule (overnight, or leave in the morning), but add a nights accommodation (with dinner and breakfast) and an extra day. They usually go for 15,000yen or so.
Another option, and this might sound crazy, is to BUY an apartment in Niigata. No joke, there are apartments there near the ski resorts for like 500,000yen or less. You have to pay monthly maintenance fees (comes to around 30,000yen a month), but then you have your own apartment, which usually has snowboard lockers and a drying room downstairs. You would need to commit to a single resort though, and work out if the total yearly cost is worth it to you: 180,000yen for maintenance, 80,000 or so for the season pass, and weekend bullet trains (10,000yen or so return)
AFAIK there is no resort provided dirt cheap dormitories that you can rent.