BTW, I wouldn't waste my money on a processor after leaving an animal ungutted and unskinnned over night. Interesting quarters with the hide still on them
As cold as it was I would not worry that there was spoilage. In cold weather I've done it several times out of necessity, and all was just fine. I've also recovered animals at first light the the next morning in mild weather.
I've often quartered in the same way, skin on as it helps keep things clean...However not if i have to pack it over a few miles, i dont even take bones then, but i aint as tough as formid
About the only spoilage i'd be worried about that time of year would be the neck.