actually, i can't really play anywhere in the winter. i just stick around at my house and putt into my basket. I cheaped out on the chains when i made it and they were double link chains and they basically rip your frisbee apart, so i had to put pvc pipe on all the chains, the final product turned out pretty decent though
I had one of those San Marino ROC's jd talked about and it cracked almost in half, it was in DX plastic and was about 40 degrees out. IMO champ plastic is not going to do that and ESP, FLX and star were all designed with cold weather in mind.
Cold does not generally hurt any of the newer discs, including new DX and KC plastic. Once upon a time, DX plastic could shatter and break when hitting trees. Although it was also more prevalent with certain molds like Rocs, Stingrays and XD's. I have never seen a driver break due to cold weather (in any plastic) in all my years of playing.
I would suggest leaving your discs in the cold even when not playing. You don't want to subject them to repeated extreme heating and cooling cycles. Plus, snow will stick to warm discs and it is harder to remove. Keeping discs in your trunk instead of your heated car or house is recommended.
The only flight differences are that discs seem to be more stable in the cold. Not sure if this is due to not being able to throw as cleanly in the cold with all the extra gear, or if it is truly an atmospheric phenomenon. But it is noticeable.