What do you know about winter sports?
Not too much! I don't really like winter. I have skiied int he past though. Do you like to ski? I went to Sun Valley once. 
I've skied only in Europe.  I'm guessing Sun Valley is in the US.
Yes, it's in Utah. What is skiing like in Europe? I've always wanted to go to Avoriaz. 
It's pretty mixed.  Avoriaz would be a good choice although I've never been there.  The best skiing is probably in Austria, the best mountains in Switzerland, and the best value Andorra 
Do you only ski downhill or also cross-country?
Downhill, cross-country is way too hard work!
What are winter temperatures there, in ski areas of Europe? It can get very cold here. 
The coldest I've experienced was -25 C in Switzerland high up.  Sorry I have no idea what that is in degrees F.
I'm actually Canadian, so that temperature makes sense- that's pretty cold. Sometimes in the Rockies here is gets to -40 C.