Donkey's, yes. Never saw a mule for that purpose. Guardian dogs....depends on the horse. Two of my broodies would kill a dog on sight.
We have coyotes and Bobcats. Have seen one bigger cat. No problems with them. The big cat could potentially be an issue but if you have easier prey and well established populations of that prey they those two will not bother them. Only time we had issue was when neighbors killed off their normal diet and then killed all of them off because they started going after anything that moved due to starvation. Once they were gone all of the prey populations exploded. It took years for things to normalize.
Neighbors dogs if aggressive are removed on sight. Stout electric with narrow spacing and low to ground helps with them.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.