I was raised to treat deer just like we treat elk. Get it hanging and get the hide off. Deer aren't nearly as critical as elk, as the heat can escape through a deer's hide easier.
However! We used to hunt over in the north central part of the state with some folks that live there. They live way, way, far away from any running water, or elecricity. They also let their deer hang with the hide on until they cut it up. They say it keeps the flies off, and keeps the meat from getting that dark rind on it that the dry climate causes over there. Their meat tastes just fine, in fact it's easier to cut up too. I honestly don't think it matters much with a deer. After spending several years hunting over there, I can see some of the reasons why they do this, but I still like to get the hide off asap.