The cold is absolutely not a problem if you're prepared. In fact, you can go too far. The hottest I've ever been on a bike is when I dressed for 15 and it got all the way up to 30. I was stripping like crazy. Only thing missing was a brass pole.
Everybody has their own way of dealing with the ice. Me, when it got extra crappy I'd go really slow and stay on the MUP, such that if I went down it was no big deal. There weren't too many days like that here.