I wouldn't leave a deer to lay unless I absolutely had to...and it must be a heck of a reason why (white-out conditions, broken leg, etc.)
If you had a less-than-ideal hit you're going to be risking stomach acids or waste tainting the meat, which will cause it to spoil sooner.
Also, a whole animal, still in the hide will retain a LOT of heat. Even in 40°F weather, it's going to take a VERY long time for much of that meat to cool to even 65°F...which means the enzymes and bacteria are going to be breaking down the meat much more quickly than meat that was properly cooled.
Larger game, such as elk, can bone sour very rapidly if not cooled immediately...especially around larger bones such as the femur. They also take even longer to cool if left to lay whole.
A skinned and dressed carcass will fair 50°F weather much better, and longer than a whole animal would.
I'd say stock up on flashlights and batteries and find those deer, rather that waiting around and risking it. A few hours of lost sleep and difficult tracking is a better deal than a complete animal wasted, IMHO.