Is is the case with most things involving growing things, the answer can be no, yes, or maybe! Apple trees need the cold in fact - that's why you don't find people growing apples in Florida. Conversely, we are pretty far north here in the Hudson Valley to be growing peaches, which is often seen as a southern crop.
We just got through a week where the temperature didn't get out of the single digits, and was dipping into the negative territory a few nights. Ideally, it's already been cold (this is winter after all) so that the trees are good and dormant. (And thus, we can prune them now.) Especially if it's a sudden change, the super cold can spell bad news for trees - more so peach than apple.
On the plus side, we got snow which ironically insulates the tree roots and actually helps protect the trees from cold-induced damage. If we get sustained zero to negative temp readings, or a super freeze like a few years ago , it can basically kill peach and nectarine trees to the point there's no fruit the following season. And that's never a good thing. The good news for peaches and nectarines here at Soons Orchards is we were able to plant our trees on a high hill, which is essentially the warmest spot on our entire farm, so the cold air falls and "rolls" down the hill. This helps the trees in winter, and especially in the spring, when cold weather or a frost during bloom can destroy your entire crop. Again, no bueno! ...and that's why my Dad always says farming is like gambling in the dirt!