Here in the South it's rare to have cool enough temperatures for long enough to age properly in the hide. The one time it worked out for me, I was able to hang a young buck for about 17 days in January. On a couple of the warmer days, I lowered him to the ground and wrapped him in a tarp and covered him with leaves until the evening. It turned a lean late-season rut-weary buck into good eating.
Usually I have to resort to quartering and putting the meat in a cooler for a week or 10 days. I put a thick layer of ice on the bottom and tilt the cooler so it can drain as the ice melts, and I just add ice as needed until it's done and I'm ready for the cutting and wrapping. I put fresh ice on the top of the meat as it ages, and I've always been happy with the result. I think it doesn't matter whether the ice is in contact with the meat, as long as the meat is not sitting in standing water in the bottom of the cooler. The ice melt has to be able to drain away.
I take great pains to cool the carcass as soon as possible. If it's cool enough to hang the deer for a while in the hide, I use bags of ice in the body cavity to get it cooled down, or I wash out the body cavity with fresh water to cool the meat and clean the cavity. If there's a stream near where I field dress the deer, I like to immerse the carcass for a while to cool it immediately after field dressing. In this region, getting the meat cooled quickly is very important to good-tasting venison.