We let them hang if it's cold enough. It probably doesn't matter too much around the rifle opener, though, if you take your deer to the butcher. He'll probably hang there for a while, too
Head down or up depends. If it's a nice buck and there are a lot of bears around, I go head up.
I don't know how much it matters. By the time the deer is hanging, any blood that is left in the blood vessels is probably congealed enough that it's not going to drain out by hanging.