Cold weather is tougher on you than on your Frisbees. You are made of flesh and blood. Your discs are made of specifically engineered plastic. So in any condition you can handle personally, don't worry about your discs.
Ok, that was the general rule. Here is the rare exception: If you happen to have a beloved, perfectly broken-in, REGULAR plastic disc (not a candy or candy blend plastic disc which, btw, are close to impervious to harm) which would be darn near impossible for you to replace, then maybe you might want to retire it for the winter. I set aside just such a Rattler for a few harsh winters because Rattlers take forever to break in. Now that I have a few seasoned backups I no longer do it and, to date, I have never cracked a Rattler.
The longer you own a disc and the more you throw it, the more valuable it becomes to you. Replacing a new disc is relatively easy. Replacing a broken-in disc is much tougher. Replacing a disc which has been in your bag for years is very difficult. Using (and therefore breaking-in) that treasured disc in the winter will usually only make it better.
Natural warping of a disc is not necessarily a problem, it is just part of the aging and refining of a disc, much like a fine wine matures. So if the top of the flight plate gets a bit wavy, don't worry about it unless it flies poorly. Unnatural warping ( being run over by a semi-truck or chewed by a pit bull or frozen in a snow bank) might ruin it. Or not. Do not be quick to discard a disc based on appearance. Throw it a few times to make sure.
A badly warped disc can sometimes be saved by bending it back into shape in very hot water.
Discs are tools. Use them. Don't worry about them. Just like you should not be overprotective of your children, you need to let your discs face the cold, cruel world on their own. I play catch with my favorite putters in parking lots with young players who have little control. Those tiny nicks and gouges are badges of honor. Gentle sanding will smooth them out and they will fly better tomorrow.
My putters have reached the darn near 2 year old mark. They are "D" plastic Magnets and both have spent overnights in snow banks. Being warped can be fixed. Being in your bag is different than being exposed to - degree winds. Crap happens. Throw your shot. there is always another disc to fill the void. No disc is truly irreplaceable.
My discs seem to become more understable. I had to take my Forces out of my bag last year because they all began flipping like crazy. I got later run forces now and they have not flipped or acted up yet. Maybe it's me, maybe it's first run discs, maybe it is the Bermuda Triangle of Michigan known as Mount Pleasant. My advise is don't wear a jacket, but instead wear 4-5 layers of warm shirts.
I think atmosphere (colder air) causes the discs to come down sooner, they just don't seem to glide as long. I know for certain that I can hit longer baskets in the cold months when I'm in Dayton or Las Vegas (my last two warmer winter destinations) than I can in Alaska from a clean tee. Me personally, I seem to lose 10% of my distance when the temp drops from mid 40s to below 30. But, the role of bad footing and effected mechanics can't be disregarded. Jerky steps lead to an inability to get a smooth pull, leads to less snap and a more stable (seeming) disc.