Doing this can either get your pup killed, or maybe you.
YNP puts out information on dogs. Bears sometimes follow a loose dog back to it's owners. This usually ends up badly for the bear or the fools who let their dogs run loose.
And that doesn't take into consideration what a loose dog can do to the critters that are lower on the food change than a dog. Plus, in YNP there are a number of beasts that higher on the food chain than a dog, and who would make quick work of said pup.
ppine wrote:
Take your dog on a leash and hike around. The NPS has a lot of rules, but usually you can bring a dog anythere there is pavement. There are also plenty of dirt roads you can use to get off the pavement and run your dog for awhile without a leash.