I haven't had any real problems with my '09 DD (original factory tires) in the Winter. But it seldom gets very cold here in S AR (the present cold snap is pretty rare). There is less traction when it gets below 45F or so but I just slow down a little bit and keep my spirited driving to a minimum. Cold tires shouldn't be a big problem as long as you keep in mind that the tires aren't going to grip like they do in Summer, ie, don't throw it into a hard corner and expect the tires to hold.
Drive like you have some sense and you should be OK. If you can't keep your toenails out of the radiator, you might be better off parking it during cold weather.
Judging by the few minutes I've driven my Z on snow/ice, it's best to leave it parked when the roads are slick.
YMMV