If at all possible, gut and take the whole animal (white tail deer) out of the woods. Liver, hearts, kidneys and caul fat get packed out in freezer bags for quick consumption - venison liver is best never refrigerated, fresh from the field. Hang from hind legs by gambrel in well ventilated cool dark shed/garage. Remove tenderloins and enjoy - venison tartare is so good it will make you cry. Once on the gambrel, 12" above the floor, wipe interior down with heavy salt solution, cleaning the cavity. Cut sternum up to top of rib cage and prop open cavity for ventilation. Hang for as long as temperature and humidity allow and to your preference. (Best I ever hung was a 28 day very large doe). Remove skin by hand beginning with the hind legs - aging will make this task less difficult - take your time and leave on any fat that you can. Fabricate into desired sub-primal parts, leaving on silver skin or fat to be trimmed just before cooking (prevents freezer burning). Vacuum seal if possible. I will usually fabricate large roasts - or whole top rounds to be used for 2-3 meals after defrosting. The more you break the animal down, the less time you can keep the parts frozen. We have two whole bone-in hinds that will feed 3 of us for a week or more.
Was exposed to the gutless method on elk hunt last year and see the necessity, but ---- the coyotes get some good stuff. Would love to shoot one close enough to the truck to take the whole beast back to a processing spot - I can imagine how good dry aged elk ribeye would be...