My own Henry mule aspires to be the sort of steady trail companion you have become, but we have hit a rather troubling wall; that of his ears going anywhere near a bridle. He is perfectly content to have the crown of a halter unbuckled and placed behind his ears, but has a rather violent reaction when anything comes sliding towards them, despite having lived 4 years in a place where ears are only lovingly rubbed. (Which he enjoys quite enthusiastically.) Perhaps you can offer up some words of advice as to how to go about bridling? Building the bridle around his head each day is getting tiring....so many buckles!
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As I see it, you can go one of two ways.
First, make sure your bridle is comfortable and well-fitted and that your mule's bit is suited to his mouth. If his comfort is not in question, then buy "Don't Shoot the Dog" by Karen Pryor. Read it. Then, when your understanding of behavioral conditioning is fully developed, buy a clicker. Use it often. Disassociate the bridle with riding by practicing often, rewarding with food, and taking baby steps. Train, train, train. Have patience. Be consistent. Break the exercise into small parts if you need to. Have you, by the way, tried sliding the HALTER over his ears? Maybe separating the bitting part of the picture from the sliding part will help him let down his guard.
Option B, which you may want to use in conjunction with Option A in order to get some rides in:
Buy a snap-over-crown mule bridle. Here are two companies that make them:
They'll save you some tacking up time, anyway.
I do wish you luck with your problem. If I had an audience with Henry, I'd tell him this—"ears are best when they're shared. If you have a good human, you can trust her to take good care of them. They're not only rubbable, but also bendable, foldable, squishable, slideable, and huggable. No human worth a lick ever hurt a mule's ear on purpose, and surely your human never will. Let the muleness in, Henry. It will fill you up from your ears to your toes if you let it."
Ears to you,