A mule is much more sure-footed than a horse. Picture in your mind, a narrow trail winding down the wall of the Grand Canyon, a string of riders on mules. Where each mule places each foot is critical. He does it from memory. The mule cannot see his feet, but he anticipates where each foot has to go as he moves forward.
Horses do the same, but the mule is much better at it.
This comes from a characteristic trait of the mule. Unlike a horse, he will not place himself in danger. If a mule decides that he has pulled a load until he is exhausted, he will simply stop until he has rested. He will absolutely refuse to continue until he rests. If a mule balks for no apparent reason, you had best look around.