If you are going to Norway you should come up here to Tromsų. Especialy in January since citys like Oslo and Bergen get a bit boring during the winter. However, its even colder up here than in Oslo. Oslo is usualy 0 - -10 in the winter but in Tromsų you get around -15.
Seeing as there is not that much culture and tourist attractions to see in the winter you should go for nature. Witch means you should go the the West Coast (around Bergen) or up North (around Tromsų). Personaly Id recomend the North as it in my opinion has the most butifull mountains and fjords during winter.
PS: In January the sun has not yet risen in the North, just so you know. Its not night dark but you wont se the sun and the days are short.
Winter in Tromsų
Info and big pic @ Wikipedia