(1) Ski - Even better if you go a couple of stops further up the Shinkansen line.
(2) Sake - Some good breweries in that part of the country
(3) IIRC, there's some sort of folk village around there where you can see old ways of life
(4) Sit in a bath and look at the snow

Much the same could be said of Nagano or Takayama, which other people have mentioned ... Takayama certainly is further out of your way, but I think it's really worth visiting. The town has some charming old streets and the sake brewery tour, which ksandness mentioned, is short but interesting. It's a real, old, brewery with some good sake.

My prejudices tell me that the quality of skiing is probably better near to MUC - but I don't really know about such things.