First and foremost.......We like mules.
Mules (and hinneys) are capable of doing anything a horse can do. They are stronger, more durable, eat less, in reality more intelligent (sorry horses), and for the most part much more loyal than any horse. A mule bonds to its trainer and will even protect them when in danger. They are less prone to illnesses, all though they can still get sick or colic, just less apt to occur.
Mules and hinneys are sterile. They can not reproduce. So no matter what they cannot add to an over population problem. Horses have 64 chromozomes, donkeys have 62, the hybrid ends up with 63. There have been a few VERY RARE cases of a mule mare (or molly) foaling but it is not the norm. The boys or Johns, are gelded (or should be) before they reach 3 months old. You really don't want the testosterone adding to any attitude they might have.
The mules (and donkeys) have a standard just like the horses do. They should be conformationally correct, balanced, straight legs/bites, good attitudes. The minis are allowed to be up to 48"-50" depending on which registry you are using. This comes from the fact that typically a "mini mule" was created by breeding a standard donkey to a pony mare. We took it a step further and are breeding a miniature jack to miniature mares.
We show our mules in halter, obstacles, barrels, poles, and are now teaching them to cart. They have the same classes at mule/donkey shows as they do at horse shows.....it's just much more laid back.
You can ask a mule/donkey/hinney to perform but they just might not feel like it
right then. My jack has been Grand Champion donkey at all but 2 shows he has been in in the past 7 years, competing against standard and mammoth stock. The 2 shows he was beaten he was still Reserve Champion. The same jack beat him both times and it was a mammoth jack.
My mares are carefully selected for conformation and attitude. Color producers are nice but don't necessarily mean I will get color. The rules change when breeding hybrids.