I intended on stating my opinion and experience, but "thebutcher" pretty much explained it. In beef, aging has merit, tenderness and flavor. In game, the meat is not marbled, it is lean. Hanging any longer than a day is a waste of time. And if you hang it long enough, it will start to slime-up.
I know a hunter that only packs out the meat, debones immediately after harvesting, it works. I still prefer to pack out the carcass, but I no longer hang. Like was said, a big deer becomes a small pail of meat if you do. Often, processing the next day isn't possible, I'd say you have a 3 day window, depending on the temperature.
Today is the day we process my sons deer, his first. It took a few years for him to harvest his first, he went with friends this year, left dad at home, I do believe I was the jinx.
Nitro
This:
"In beef, aging has merit, tenderness and flavor. In game, the meat is not marbled, it is lean. Hanging any longer than a day is a waste of time."
My butcher wants it ASAP if it stays in his cooler for a couple of days there so be it.
For me I shoot, gut in woods and get it out of there, de-hide it ASAP, much easier when the deer is still warm and as soon as the hide is off the meat starts cooling, it's hanging maybe a day to set up and allow me to pick any hairs off then its off to the butcher.