With studded tires, anything is possible.
http://www.youtube.com/watch?v=luBIaBXM4iU
On a marginally more serious note, not all places on earth have what you'd call a winter season, complete with subzero temperatures and snow. 12 hours of sebring runs during winter (at least what google calls winter), for example.
RicerDude wrote:Wouldn't their hands get really cold in a 200mph freezing wind? I can't imagine fireproof gloves insulate that well. I mean my hands get pretty cold just riding my bike in the winter.
Why wouldn't fireproof gloves insulate well? They're designed to protect you from fire, which is a slightly different temperature from what human flesh should ideally be. Besides, the cockpit of an F1 car is usually a pretty toasty place and they be active while driving, which helps circulation to the extremities. It wouldn't be that bad.
@OP:
standard tires will struggle to develop temperature on tracks, even just above freezing. I suspect that they would tend to understeer on entry and oversteer on exit, less because of car balance and more because there's just no grip. of course, studded tires solve all problems, except for that of the angry circuit owner with a repair bill after you tear up his asphalt race track.