You can get away with a lot, although there is a difference in meat quality (in my mind) between "getting away with" and being prepared for the worst.
I wouldn't throw that deer away just yet. Process it, get the hide off, cut into the larger cuts and see how they are. Even if not perfect, you can grind it and use it in chili and stew etc, with spices to flavor it. Make sure it gets cooked well.
While in Asia and some of Europe, I would see butcher shops with small animal carcasses hanging at ambient temperatures.
CHuckC