After the kill .... if at my camp, gut it ASAP and hang in walk-in cooler. I am a firm believer in getting the meat cooled down as soon as practical.

If not hunting at my camp, I'll carry about 20 gallons of fresh water and 2 large coolers filled with ice. I have one of those "skinning racks" that attaches to the trailer hitch receiver. I hang the deer, get it gutted if not done in the woods already and skinned ASAP .... and the wash down good with cold water. I use a hand pump sprayer to wash the skinned deer thoroughly. If it is cold - 35F or less, I'll let the skinned deer hang for hours until it cools off. If I am hanging it over night, I leave the hide on. If it is above 50F or so, I definitely get right to it. Take off the shoulders, remove the back strap and inside loin, butcher off all of the neck meat and split our the hind quarters. I keep the liver if it is not shot up. Put the meat on ice and haul the remains to the woods for the critters to use.(If at my camp, head to the camp's "gut pile".) I leave the cooler drain open to let the melt water run. And I check regularly to make sure the meat stays iced up well. I usually carry it to a processor near where I hunt.