A more simplified answer to this would be a higher compression capacity within the compressor chamber. Cold, dense air with moisture has a higher rate of expansion than warm, less dense air without moisture. I wouldnt put moisture into play because it also affects lift, but comparing volume by volume of the two varieties of atmosphere, the cold and moist dense air provides the greatest rate of expansion for thrust producing turbofans.
If I remember my physics correctly (and its been a while), temperature is directly proportionate to pressure. I would think that sound wouldnt be able to travel in a zero pressure environment, but I cant back that assumption up. You are correct about temperature being regulated mainly by the temperature.
<---not a physicist.