I've not ridden in winter since I went to school, when I used to arrive with ice in my hair if I hadn't had time to dry it after my shower. I was riding 23c then. If it got really cold I used to use my brother's MTB with knobbly tyres. The width seemed to make a bit of difference, but I suspect the fact that I was slower made as much difference.
How much difference do winter tyres make on a bike? I use them on my car, but that's heavy and we live on a hill. I currently have 38c Vittoria Randonneur Cross tyres on my commuter (because they were cheap at planet x) so they're wide-ish and have some grip. Would I notice much difference? I do also have my MTB with knobblies on, but I guess on ice it won't be much different, although it might be better in snow?