Sport quads will work fine for almost all the trails in the Bighorns with a few exceptions.
Have you decided what area you want to see in the Bighorns ( North or South)? Either side offers great ATV trails. Are you planning on staying in a town (Buffalo or Sheridan) or prefer to stay on the mountain either by camping or staying at a lodge?
The South side is my preference only because we live there and its close for us. Both sides have great ATV oppertunities and views. There is a place in Buffalo that rents ATV's and campers, they will take them up the mountain and have them waiting for your arrival if that intrests you.