The idea is to have an individual accomodation near a small village where we'd be able to do activities like cross-country skiing, sled dog, snowmobile, etc. while being as much as possible away from the large touristic areas.
Starting point is cross country skiing is more available than dog sledding in the southern part of Norway. If you want dogs and snowmobiles you will likely need to go to the northern areas that are less restrictive on recreational snowmobile use such as Finnmark and northern Troms where the county governor may at the proposal of the municipal council issue regulations on the right to use snowmobiles during the period when the ground is snow-covered, along separate trails on uncultivated land and ice-covered watercourses.
If you can live without snowmobiles, much of Norway is very cross country skier friendly. We have enjoyed:
Høvringen as a gateway to Rondane National Park. The village is accessible by train to Otta then bus or car service to the village. My preference is lodging at Smuksjøseter Lodge. Smuksjøseter is a 5 km ski or a Canadian Bombardier Weasel ride from Høvringen.
During the winter season there is a direct bus service from the airport direct to the accommodations in Høvringen: http://english.hovringen.no/
The Hardangervidda National Park is ringed with overnight accommodations that would be good base camps for ski exploration of the plateau. A number of the mountain lodges are accessible from the Oslo to Bergen train line with train stops at Geilo and Ustaoset being good jump off points into the Hardangervidda. Lodging is available in walking distances from train stations such as Geilo (Geilo Hotel) or Ustaoset (e.g. Ustaoset Hotell) or a short 5 km ski from a train station (e.g. Tuva Turisthytte). For other Handagervidda lodges: http://hardangerviddanett.no/en/mountainlodges/
The Jotunheimen National Park is a more rugged alternative to Hardangervidda, being the mountain home of the giants. Winter access is a bit more complicated. And dog Husky tours are available in the Jotunheimen but I don't have person knowledge.
Check with the DNT touring association for winter advice.