I've had to leave a couple animals out overnight, but it was cold enough to not worry about meat spoilage. Overnight lows were anywhere from
-10 to -40 degrees. To keep predators away I've left my sweaty undershirt hanging from a branch nearby and haven't had any issues with animals coming in to have an easy meal.
I have also passed on shots knowing that I wouldn't be able to get the meat out without it spoiling because it was too warm or if I couldn't get to them in the pending darkness. (I don't sleep well if I haven't recovered the animal and gone back to camp.)
I have had to leave animals over night, more or less becuase of location, lack of help, etc. I hate to have to do it, (it seems like all I do is worry about it if I do) but if done properly, it never seems to be a problem to the meat IMHO. I have always quartered them out, to hang if leaving them overnight. I can usually have a deer quartered and hanging by-myself in a half hour, no problem. I usually pack the head/cape and back straps out with me, or a quarter. Then the following day all you need to do is grab a buddy and one trip, your done.
Here is a link if anyone is interested to the gutless technique, it shows pics and good detail to someone interested in trying it out.
I have left two elk in the field overnight and came back and got them the next day. No meat was wasted and no moral or ethical problems as far as I am concerned.
You want to make sure you get it dressed and the body cavity opened up for cooling. If you can get it quartered and hung, all the better. I usually carry about 150' of bailing twine with me in my pack to hang quarters if I have to.
Bottom line is, can you save the meat? if you can then you're good to go.
If I know it will freeze overnight I have no problem leaving a animal overnight. I always try and gut / skin before I leave it. If I know I am going to mount it, I will only skin to just infront of the shoulders (in the dark I have bed aim...and it costs money to get holes stitched up) so that the meat cools off. If it is going to be hot overnight I try and get out as much as I can. I left a large whitetail overnight at minus 30, I bent the legs into handles so when it froze it would be easy to load onto a quad. It is amazing how easy a deer is to move with handles.
We almost always have to leave elk out overnight because it usually takes the better part of a day to get one out with horses or mules. That said, I don't leave until they're skinned, quartered and hung. About 15 years ago I left a 5-point bull out overnight. I split the brisket and propped him up over a log with a stick wedged in his chest to open him up as much as possible. I left him at about 3PM. It snowed about 2" that night and I got him home whole the next day by noon. While skinning, I could start to smell the bone sour in him about 1/2 way down. The whole front half was spoiled. I don't care if it takes me until 9 at night, they're quartered, skinned and hung when I leave them. They're always perfect when I get back. I've had wolves walk within 10 feet of hung and skinned elk and they didn't bother them. I think the more an elk looks like an elk, the more chance that a wolf will get into it.
All of the above comments have good merit. A lot depends on location, animal type and size etc.etc. That being said I have been involved in leaving deer, elk, moose, and antelope overnight many times. A lot of times it's for more than one night at the kill site. Most of this involves being here in Montana in the backcountry and being a 6-8 hour pack trip to a pickup or trail head. We gut an animal, quarter it, try to get the quarters off the ground on a downed log or large rocks, brush it up with tree limbs and head to the wall tent. We have more potential from birds i.e. magpies, camp robbers, whiskey jacks or whatever you want to call them than anything else. We are dead center in the middle of both black and grizzly country. My experience is if you quarter it and get it off the ground, it'll cool down dang quick - much better than being in the back of a pickup and I have yet to have any bad meat. In the early backcountry elk season, Sept. 15th, and things are really warm we will bone it out into meat sacks, put some lodge pole pine across a creek in a shady spot, and place the meat sacks on the poles - preferable 4-6" above the water and that meat will cool down faster than anything and will be almost the temp of the cold water in short time. The thing I think is most important is to have a plan beforehand in whatever area you are going into for a downed animal.
I used to manage a wild game cutting operation and have seen game in every condition possible and in many stages of spoilage, all which is preventable by doing a few key things.
It all starts with gutting, remove the whole windpipe and all the contents inside the pelvis, air need to move free up through the carcass the bladder must be removed.
I always carry rope and light game bags to deal with game. Deer I just pull them up into a tree by there hocks or lay them over a sage brush, just get air under them.
Elk get quartered with the hide on hung then skin one side and remove flanks, backstrap, and neck then roll over and repeat hang in bags.
Elk start to spoil in three areas, the neck, between the shoulders and in the ball sockets on the pelvis.
The worst things to are not remove the windpipe and bladder, let snow accumulate on carcass, haul game under a topper and let the sun get to it.
Antelope get skinned and under water as fast as possible for best quality, deer and elk do not skin till they are ready to cut and cut them as soon as possible.
Wild game flavor gets stronger as they dehidrate, hanging for a long time and skinning dehidrates game fast making them stronger tasting.
I used to do seminars on game care and had a detailed post but my daughter has just figured out the mouse and she came up and started clicking and it went somewhere.