Leaving flat screen in camper over winter

Electronics in general are not very sensitive to cold storage temperatures and even cold temperature operation. The display may not work as well in the cold, and there's a very slim possibility that the digital electronics would not operate properly at all if they were of quite marginal design, but I very much doubt that any lasting harm would come from cold temperature operation. Many car radios have color LCD displays, using basically the same technology as the TV, and they sit in cold vehicles all the time and are used at all sorts of temperatures.

At any rate, storage under winter temperatures when turned off will not cause any problems, at least assuming you're not in Alaska or someplace similar.