I think your temperatures may be too cold. It sounds like the deer will probably cool down and be frozen by tomorrow morning. You aren't supposed to freeze and unfreeze the deer. Now don't get me wrong, I don't think thks is going to ruin your deer and that you will need to throw it away . . . just that this is less then preferred, optimal treatment. Let's hear what others have to say. Maybe more well informed people will say I'm full of 3hit.
Alsatian, we regularly let them freeze solid with the skin on then dont even worry about them untill they start to thaw, never had any problems with the meat, it actually seems better then the ones we kill early in the year and must process the same day without freezing.Weve done it since I was a kid and never had any problems.