We had ours! We kept him on a leash, but we were there during rattlesnake season. In camp he was off his leash as there were no other campers close and he sticks around.
It’s a spectacular place, hope you make it there. There is a USFS and BLM office right in Bishop, they will give you the rules and regs, and they will give you maps of the best places, super helpful. Good luck, it’s the most magical place.