Why not.. I have debated getting a little Chinese made 110 four weeler.. Can't put a deer on it, but it could drag a sled with a deer on it.. Plus it can go around, under and through tighter spots.. Put a great silencer muffler on it and you can zip around almost anywhere in the woods quiet as can be. You don;t even need logging roads. It'll fit through most timber around saplings and such.
Why are you going to buy a cart to drag a deer when you could buy a little weeler to drag it for you..
I don't know what model it is but my dad has one that looks like the picture in UK's post. Obviously it's better than nothing, but quality is fairly poor. We pulled two deer out with it in S.O. this year... worked "ok" on the first one... second time the wheel fell off before we even put the deer on it. Cheap ass pin fell out, then the wheel fell off, and we lost the pin and both sets of bearings... rendering the cart useless. Whichever way you go, make sure it's got a good set of wheels/hubs on it. Either that or do what you can to reinforce the cheap ones. I've seen the plastic wheels break over bumps and rocks before, too.
I have cheapie one and its better than nothing. It has smaller wheels and a narrow wheelbases that on a side hill gets kinda tippy. It is still wayyyyy better than dragging. If you get one spend the extra $$ and get one with a good wheel base and bigger tires.