^ This! I do not think many people understand the difference between deer / pork and beef. Many times, we ground up pigs (pork) for sausage, that might have still been a bit warm from the butchering - there is no "marbled fat" to worry about. Same with deer. But it is nice to be able to hang good beef for 8 or 10 days after butchering - at a temp that keeps the meat cool but does not freeze - I had read that circa 4 C or so is about ideal.You could hang in your garage if it was cool enough, unlike beef there’s no definitive gain from hanging/aging deer. There’s no fat marbling the meat, you’re just drying it out.
I generally let it rest overnight if I’m too tired to butcher it right away, or if it’s warm out I’ll break it into quarters and leave it on ice in a cooler for a day or so till I have time to cut and wrap.