I'll hang a deer for up to five days if it doesn't get over 40 degrees. (Last year I actually left one for 10 days... but it was frozen solid for the first five days)

I'm not sure it does much for flavor, but I do think it makes it more tender. If I can't hang 'em, I'll keep the meat in the fridge or a iced up cooler for a couple days before freezing it.