Under the circumstances you describe, it would be better to have left the skin on it. This would keep the meat under the skin protected and moist. It may make the skin more difficult to take off, but not terribly so.

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.