As soon as possible. I hunted in WI once and talked to a old butcher. He told me to not let them hang to long and to get all the fat I can off the meat. He said hanging to long and fat can make deer meat stronger, because it wild meat not a cow. I cut mine up and put the meat in ice water to stiffen it up for cutting. I have maybe have cut up over a hundred deer in my life time and I never have had any bad deer meat.