I am not a horse or mule person so forgive the ignorance. Why do you take the shoes off?
The hoof grows at a rate that a horse or mule needs it hooves trimmed about every 8 weeks + or -. depending on the animal. If shoes are left on,the hoof will tend to grow out over them. If the shoes wear out,the nails holding them will eventually wear off and the shoe can come off at angle that might pull sections /chips out of the hoof.
.Letting them go bare foot for awhile lets their feet grow out naturally and wear naturally. You shoe horses and mules for traction, protection, or correction. If none apply let them go barefoot. During winter or off months most don't need shoes.