Those aren't muzzles, they are a training device called a Halt-i (tm) or sometimes a Come-a-long. Patterned after a horse's halter, the basic premise being that a dog will go wherever its nose is pointing, so rather than use a pinch collar/chain around the neck a gentle alternative is this device. If a dog pulls, rather than get its neck squeezed, its nose gets turned in the opposite direction of where he/she is trying to go, so eventually the canine learns to go in the direction the trainer is leading, as opposed to the dog trying to lead, and there are no harsh corrections with the leash. I used one with my very determined Doberman and it was the only method that got her to 'heel'.