There is something wonderful about being outdoors in winter, but not everyone loves downhill skiing and snowboarding. Nagano has a number of cross-country ski areas that offer a good work out and wonderful views. In general, I have found the courses a bit more difficult than courses elsewhere, but not impossible for a beginner.
Nozawa Onsen is in northern Nagano and has cross-country skiing, but the rental is very difficult to find and along the main street, away from the trail. The course is nice and was used in the Nagano Olympics.
Kirimagane is south of Matsumoto outside of Suwa. From Matsumoto it takes about 2 hours to get there. Ski rentals are available. There is one well-groomed beginner course which has a view of both Mt. Fuji and Suwa Lake on a clear day. There is also a network of trails further up the road which weave around the area. These are a bit more difficult but peaceful and remote.
Minegata is in Hakuba and is about 2.5 hours from Matsumoto. It is a small remote resort but very nice and peaceful. Ski and snowshoe rentals are available. You take the lift to the top of the mountain (600 yen round-trip) and there is a 5 km track with small hills along the way. The views from the top are good on a clear day. It is also possible to take a trail to the bottom of the mountain rather than take the lift down.
This website has directions to the resort and information on more courses in the area.