It depends, of course, on how much snow and slop you go out in, the temps at the time, and now much ice is involved..

I can't speak to cyclocross tires, but I run studded snow tires on my bike. Yes, there's a certain peace of mind component, but that's because I can feel the cleats and studs digging in. For the most part, I don't have to change my riding style, and most of the time, I have better traction (and therefore control) than cars do.