RE: Cooling ?
I agree with most everyone else. The hide is best left on until you are ready to butcher. As far as the freezing part goes, from what you stated, it probably will at least semi-freeze. Not a problem in my mind. A deer is much easier to cut up when partially frozen anyhow. If it is solid, you will want to thaw it until you can "work" the meat, but not totally thawed. It is much easier to grind partially frozen meat. Meat gets frozen/thawed regularly. Don't worry about it. It'll be OK. I'd worry a whole lot more if it was left in temps of 50 deg or more for a period of time...........