Good points... let me work myself through this... Let's consider my hunt last week. Let's say I killed one right when I was going to leave on the night in question. Now, I have an elk on the ground, it is still dropping heavy, wet snow, and I am already slightly hypothermic. How would I handle that?
First, I would realize that I am in for a long night. I would probably do some jumping jacks to warm up a bit. I would build a simple shelter and start a fire. I would drink some hot liquid to warm my core. Then, I would get to work on the elk. I would use the warmth of the elk to keep my hands warm. The work of breaking it down would probably keep me warm.
If I was warm enough, I would break it all down and hang it from an improvised meat pole.
If I was too cold, I would gut it and break open the hips to cool the meat down.
In either case, I would probably leave the meat in the woods. I would hike back to camp and sleep. I would come back in the morning with an empty pack to starting hauling the meat out.
Once the meat is hanging, I personally would not haul a lot of meat in the dark especially if bushwacking. It is going to take me several days to move the meat alone. I don't see a real difference between it hanging at the kill site or hanging at camp.