May I suggest one of those poly slip sheets as well.
I carry a really heavy duty space blanket (a military casualty blanket) that has been used to skid a few deer out of the woods but I often carry a 5x7' blue poly tarp for the same purpose.
If you tie the front legs of a buck to the base of the antlers or the front legs of a doe to the upper part of the neck right behind the head it streamlines them a bunch and gets the front legs out of the way so they don't hang up on every tree or root in the woods.
When dragging critters out I usually take my coat off, put on my orange vest and carry my rifle/shotgun, pack and coat ahead leaving the critter behind. After 50 yards or so I put the stuff down and having used the opportunity to scout the path of least resistance I go back for the deer.
This lets me get frequent breaks and follow the least obstructed path out to where I can load the deer up.
Lance