Going from warm to cold will not cause condensation, but once the transmitter is cold bringing it back into a warm environment will cause very bad condensation. I am very familiar with this because I used to do mountaineering with very nice cameras and it is a huge problem. The condensation can be almost entirely eliminated by putting the transmitter in a plastic bag and vacuuming out as much air (and therefore moisture) as possible before returning to a warm environment.

Of course this addresses only the moisture issue... how the cold affects batteries/electronics is another matter I can't help with.