I've hung meat, quarters (elk and moose) and whole (deer and antelope), with the hide on, when it is cold out. When it will freeze at night or be close. One big WT I shot in SD at dark, just gutted, cold as heck, left it draped over a log. It famously froze solid, had to hack saw legs off to fit in PU with canopy, -15 in early Dec will do that, still hear about that one.
The hide can help keep it clean transportating it out in some cases, others just flat ran out of time and was cold. We sometimes skin them when we get them out or maybe the day after. One Moose was gutted, cut all the way to the jaw bone skinned a bit down the neck, pelvis fully split, hide slit and skinned a bit on each ham, and front quarters partially opened, layed on it's back with a couple sticks under it overnight. He was shot about an hour before full dark. Quartered and transported the next morning, skinned and in meat locker by mid-day, meat was perfect. Was Sept in WY at about 8,500', low to mid thirties with some wind that night. My sons Moose two years ago, was skinned and hung in a locker within 3 hours. No difference in meat quality.
Another was an antelope in MT, first time I did not skin fully, late Oct/early Nov, lows in mid 20's, highs maybe 42-44. Shot and just gutted. My buddie, a MT native, said leave it in the truck, I was suspicious, pitched a bit of a fit, then figured he's been doing this for 50 years and that was my first Antelope, so shut up. 3 days later delivered to processor, skinned at that time, the meat was excellent.
Couple keys I learned from the first MT experience, the carcass was fully chilled due to weather conditions, skin flaps trimmed away so it is not tainting meat. If not super cold or cold and deer or smaller, I do partially open them up. While I prefer to get it fully skinned and swinging in the breeze, and we usually do that, if weather is right, I simply have not found it to be an issue if done properly. Probably done skin on 10x or so in last 25 years.
My experience anyway.
