Hi Norway Fan. Tromso is definitely getting some snow right now in December. It isn't huge amounts but definitely snow. And quite cold - rarely above freezing. You should be aware that right now Tromso gets 0 hours of sunlight during the day. (The up side of this is that you get almost no darkness during the height of summer.)
A friend of mine was just up in this area and she saw the polar lights every day (again, because it is dark 24 hours a day you get to see them even at 11 a.m.) But it is, like the weather, variable. There are times where they aren't visible at all.
I hope this helps.