Similar to Hunting Man's expensive steak, I've always heard the longer you hang the deer, the more tender the meat. Our family doctor hangs his deer at least a week. I'm no expert on venison, but with beef the aging process allows the collagen in the muscles time to break down (increased tenderness), and provides that "aged" beef flavor. The only downside is that you have more trim loss. We hang all our freezer beef for at least 14 days. Heck - one year we hung it for 21 days.
One of the big challenges we have here in the SE is the big changes in temperature. Bacteria can't work if temps are below freezing, and you don't want the temps to get to high (much above 40 deg).
Maybe venison, being leaner than beef, doesn't need to age as long? I'm not really sure. I've heard leaner beef carcasses are usually hung for a shorter length of time to keep them from drying out too much. That being said, muscle fiber and collagen can't be all that different between deer and cattle. I'd bet aging venison for a few extra days would produce a more tender carcass.