It's interesting because 5 years ago you would have gotten a very different answer. I've found that the new plastics in general are more resistant to cold and heat, however, some of the blends will warp. My experience is that affects their flight way less than warping of the old plastics (DX) abd some of the "Pro" blends.
Regardless, If I store my discs in the cold or heat, I lay them flat, or stack them carefully so that they are less likely to warp.
I've been thinking about this as well lately. I've just started using the softer plastics like FLX, Star, SS or SSS from Gateway or some of the others that I don't recollect at the moment. Either way, you should be fine to throw most of the plastics these days and not have to worry too much. I'd just we a little worried for some as it approaches 0 or below.
I cracked a Cryztal Challenger last winter.
I don't store my summer bag/favorite discs in the car in the winter. I imagine it is stressful on the plastic, same as in the direct sun, and can cause damage over time.
Cold won't hurt the discs at all. I prefer to leave my discs in the cold in the winter so that when I'm playing they are not warm enough to melt the snow. On the way to the course i leave them in the coldest part of the car for the same reason. The snow will stick more to a warm disc than a frozen disc.
Cold plus hitting a tree can certainly hurt the cheap plastic. Severe cold and hitting a tree can hurt even the good plastic. Cold and bad stacking can hurt a disc, but there it is more the bad stacking.
I keep my discs in my car all winter (and spring, summer and fall) because I am too lazy to carry them in to the house. I have zero concern that a candy disc will break due to cold. Candy plastic will slice but is highly resistant to breaking. So a razor blade or a knife can cut a candy disc easily but you can throw a candy disc into a brick wall as hard and as long as you want and the disc will last longer than your arm (the rim will gouge and scuff).
If anyone wants to take this bet, I will put up $100 and supply the disc, (even a Crystal Z Challenger).
I use stick-um on my discs to help with grip. When stick-um gets too cold it doesn't stay tacky. So in winter, on the the drive to the course, I put my discs on the dash board and turn up the defroster. The heat regenerates the tackiness. But when they get thrown in the snow they get cold again, right? Yes, but at least they start out tacky and retain some of it for a while. And a heated but unthrown disc, even once it gets cold will retain a bit of tackiness. So I purposely keep a couple discs in the bag I do not throw until late in the round. I also warm up with backup discs to keep the starting lineup tacky for longer.
As Bruce mentions, when a warm disc lands in cold snow, the snow melts and gets the disc wet. True and it is a pain but better than throwing slippery discs forehand (I'm a forehander).
My dashboard heating trick eventually warps the flight plate of the discs a bit. I cannot detect any difference in flight characteristics from this warping. I have candy discs which have been in my bag for years and have been reheated numerous times (hundreds) without harming their effectiveness.
I am very careful with my putters (D "premium" plastic). D plastic, once it is warped BY HEAT, may be harmed (heat creates plastic memory so I'm concerned it might alter that memory). So the putters get heated less and are carefully stacked on the dashboard.
Something I am looking for but have not yet figured out is a way to keep my discs (even somewhat) warm in my bag during a round. Other than handwarmers (reusable or disposable) does anyone have a solution for this?