I haven't used sleds with runners, like the kind we rode on when we were little kids. ( After you get too old to ride those things, they're best used for ice-fishing.) I have used the semi-stiff yellow plastic things that kids play with in the snow. It's kinda hard to keep a deer carcass on the yellow sliders. Ditto for toboggans, especially in steep terrain. Neither work quite as well as just wrapping the animal in a sheet of visqueen and duct-taping it together. ( Make a tube out of it around the carcass, two layers thick. A couple of wraps with a bungee helps to keep the plastic in close to the animal. This doesn't hurt a thing, either.)
This works great on snow, of course, but they do tend to get a little out of control going downhill, since the stuff is just so slippery. If it's a big, bony-headed warrior-buck, you could get run over and gored. ( Don't ask me how I know this.) On wet leaves it's pretty good, too, and on dry ground it's somewhat better than the hair on their hide. When you get to rocky soil, though, it wears out the plastic pretty quick.
Nothing like a wheelie-cart for dry ground, but they're also a pain in the neck to pack in, with all the other stuff one has to carry around. On the other hand, if you're packing in a camp, a game cart may be worth it's weight in gold. We have used them for that, and every time I've had to make an extra trip to camp to get a cart to haul out a carcass, I've been glad I did. Mostly that has been when the ground was dry, and it was easy walking but hard dragging. In situations where the visqueen dragging works well, carts with wheels on them typically do not. The wheels get clogged with mud & slush, and just sliding the animal out in a plastic sheath works so slick that it will make you feel smart. It also packs pretty small on the way in.