The military use of mules is probably the origin of the tradition of roaching the mane, which is done to all U.S. mules (or part of it, the other reason being that mule manes tend to be ugly).

It’s also the origin of another term. Large mule strings (the Grand Canyon still do this) would indicate a mule’s training by the number of layers in the tail…one for pack, two for pack and saddle, three for pack, saddle, and harness.

An untrained mule would have its tail trimmed short, hence the term for a new or inexperienced person: Shavetail.