I've always hung my venison as long as I practically can given the weather. By that i mean i have hung deer for two weeks out under a spruce tree in November with the hide on, and i've also hung them in the barn for a week with the hide off.
I've done road kill deer, same day, because I had no place to hang them, and i've cut them up and "hung" them in an old fridge.
I came to the conclusion having had both great meat, and tough meat from all of the above, that there is a lot you can do in meat handling, and a few things you have no control over.
IMO, ..Getting the guts out and the hide off asap is the very best thing you can do to help your meat unless you remove the meat at the kill site guts in. Probably hanging 24hrs is all you really need, to allow rigor mortise to fade, and the meat to relax.
Hanging does not mean it has to actually hang! If you simply put the meat on racks in an old fridge it works for me.
Meat that has been hung with the hide off, and is dry on the outside is a hell of a lot easier to work with than slimy meat fresh killed.
Road killed deer sometimes are filled with blood, as they may die with minimal blood loss. hanging them becomes much more important. Consider hanging individual quarters to let the blood out.
sometimes you just can't win, and all that effort will still result in tough meat. Now and then it happens, don't give up, the tender cuts are worth it. Why that is may have to do with the age of the deer, the fact it's a well rutted buck, or maybe it's pumped up with adrenaline as a friend tried to tell me. But if that were the case, the tree stand does shot would always be tender, and although they tend to be, you can still get a tough one.
Some time back I shot with a crossbow a really big buck on Fogduckers place. There was no fat on that old buck at all, nothing inside or out, plus he wore battle scars of a long rut, it was the last day of the season. I damned near ground the works expecting it to be tough. It wasn't, it was exceptional.
It was very cold, and i had a time gutting and dragging it out myself in a foot of snow, but after a half hour drive home, i hided him, and hung him in my garage for a day, until he went to the butcher who hung it for a week. nothing exceptional in that meat handling, yet the meat was perfect. You win some you lose some, last years crossbow buck, a young one, is tough.