In reply to F_D:
I live and climb a lot in Jämtland. The weather right now is rubbish - warm and wet - although the hills are sure to have snow and still ice. Most of the posts here are right - the main deal is rolling hills, a lot like the Cairngorms. However, there are some real gems. Sylarna is the most obvious and the climbing potential is massive - not a lot has been done there. The traverse is one of the great mountaineering days out, but to get to the mountain station is a 16km slog. I'm not sure it is open in January, but most have a winter room. The traverse itself is technical in places, but only up to Scottish 3 at the most. And you can bail off it in many places as well. As the other posts say, skis are pretty much essential although there is not a lot of snow right now. If you get a dump though, and are on foot, you are in trouble.
The other great place is Lunddörren. Access is a problem in that it is again a 25km round trip just to get to the climbing. In the pass itself there is a lot of ice, but maybe January is a bit early, especially with the poor winter so far. I was there a month ago and it was bare - we walked in and climbed a 300m grade VI,5. In and out in the day was an 18 hour round trip! I usually go in with hear for a weekend, but that involves skis and sledges.
Basically, it is Scottish climbing and Arctic conditions which is a full on combination. If you have decent experience you'll be fine, otherwise I would stick to the lower level routes. The Jämtland Triangle goes between mountain stations and goes through some amazing Arctic scenery. January may be too early for the stations to be open. Check out Storulvån, Blåhammaren and Sylarna mountain stations for the full triangle.
Otherwise there is good low level ice climbing about 45 minutes to an hour from Östersund which is always worth checking out. Offerdal and Klövsjö are the best.
Good luck with the weather. It can get down to -30C, but at the moment it is about +5C! Down to -8C at the weekend though. Who knows what it will be like when you come?!?
Good luck!