I've got a cart that I made with lawn tractor tires that is great for a long haul. The commercial ones with bicycle tires bog down and are hard to pull on soft ground. You may be able to put wider tires on the commercial ones with a little modification.
In central Florida where I grew up, the deer were small and we would gut them, cut a hole in the hock like you were going to hang him on a gambrel. Then you take the front legs and pass them through the holes in the hocks, cut the knee joint on the front leg and push the bone out of the hide to make a tee. Then you can bend down, put one arm through one front leg and one through the other and put the deer on like a backpack. With a small deer, it's really a great way to carry them long distances, just make sure you're covered in orange!