Yes I've used ATV'S to hunt. Depending on if your limitations are temporary or permanent I'd look and see if the state you're hunting has a special license class. These generally allow you more latitude on where you can drive, how you carry the firearm etc. They also provide folks helping you retrieve-some flexibility, say if a finisher is necessary and you can't get there.
Long Range Hunting lends itself fairly well to this type of hunting. Good optics, a good chair comes in handy, a shooting mat, a tarp to cover gear, or yourself. Probably the tough part is the recovery phase make sure ahead of time whose available to help. I've been blessed with good guides and good friends that have made it possible to continue this activity. Folks that planned the mountain, and carried my stuff all the way to the goat country and back.
At the end of the day-slower can work for you. I've got a whitetail on the wall that thought doubling back on the fast guys was a good trick.