The most important thing, even more than hanging or cutting the throat is gutting it. That's the source of bacteria that will spoil the meat. Ideally the animal should be gutted within one hour. By then is when the bacteria are getting out of the gut and tracking up the blood vessels. Also if you have to delay the butchering, don't skin it. The skin is skin tight and already designed to keep out bacteria. Hanging will help it stay cleaner and if hanging high enough will prevent critters from getting to it, but from a purely culinary standpoint isn't absolutely a must. Drachen alluded to this in the "dressing", but it depends on which author you read whether dressing includes skinning.
If you do delay skinning for such a reason you will want to wait until rigor mortis is over. Trying to skin an animal that is in rigor is much more difficult. A deer will be easier than a boar since deer have less connective tissue holding the skin in place, but still. The heavy rain (as well as the cold) will also keep flies off it. Whenever possible I prefer to butcher in dry cold.
George beat me to it once again. I would add that not gutting it, aside from a massive bacterial issue, will keep the back muscles and other areas piping hot for hours (especially on a large animal, even in the cold). They have all that insulation for a reason, and the gut is just a big fermentation vat in these beasts.
Most hunter education courses teach "slitting the throat" is useless on a dead big animal and actually spoils meat by allowing access to dirt and insect.
Minutes after the heart stops beating, blood will not "drain." At this point, the hunter would need a mechanical pump and replacement chemical.
Throat-slitting is the usual process for killing and bleeding out farm animals whose hearts still beat and will pump out arterial blood for a short time.
An exception in hunting is the big game animal still "alive" from a shot not immediately fatal. Such rarely happens with an arrow, the main job of which is to kill by internal bleeding.
On most big game, slitting the throat only soils good meat (as does remaining wet for and considerable time). As said, cold is good for preserving meat.
Not totally true. Blood flow/drainage will slow significantly after the heat stops, but all those major vessels can still hold and release a ton of blood. Yes, there's nothing pumping it along, but gravity an an opening in a major vessel(s) can do wonders.
And rather than slitting ear to ear, you need only jab the jugular AND carotid. You can do this after you've dragged it somewhere, but if you do it before, just cut off the area of meat around the area you've contaminated with your open wound.
Funny enough, it's easy to hang an animal after it's gutted but it's easier to gut an animal (imo) after it's hanging.
