The E5 train is scheduled to start the Hayabusa service to Shin-Aomori in March 2011; so if you want to ski and see the snow monkeys in Nagano, you can take an E5 until Omiya and then transfer to the Asama service to Nagano. If you want to ride it for longer at its top speed, you will need to split your trip in order to accommodate a trip to Sendai or Aomori.

As for skiing though, there are quite a few slopes in Tohoku that somewhat near the Shinkansen, both in Fukushima and Yamagata. However, I'm personally unfamiliar with them. I always found Ski Japan Guide to be useful though, you might want to take a look.