We leave the hide on as well, partly because we hang outdoors. Keeps the meat clean, the snow, pine needles, or bugs off, and keeps it moist. It's not that hard to skin, even after a week and a half.
If it were really warm, I'd take the hide off, let it hang over night, and do the cutting in the morning, or when the meat started to warm again. Once the meat is cooled, you can get away with a short period of warmth, as long as it's not in full sun. We hang under some big spruce.
Another trick, to let it hang a bit longer is to jam a bag of ice or two in the cavity.
Remember, it's the meat temp you are watching, not the ambient temp.