Equinauts?
Astrohippos?
I remember reading a SF story about a person who grew up on the moon and at one point they mentioned having seen a horse in the zoo.
Could you train a horse to live on the moon?
No-place else than the SDMB…never did I imagine I would read that phrase.
I bet Heinlein or Clarke could have written a good story based on that, though.
Issue–how do you rig a couch for acceleration out of Earth’s one G?
Without killing the horse, or crippling it?
Sedate it, lay it on its side on a soft-ish surface, and away we go.
By the time we have a permanent colony on the Moon, we might have an orbiting space station, either a Von Braun Wheel or a Stanford Torus.
Why stop at a single ring? It could have an outer ring, simulating Terran gravity, and an inner ring, simulating the Lunar gravity. There could be several intermediate toruses (tori? torodes?) where people (and animals) could gradually acclimate to lower gravity.
Maybe transport a horse embryo in an incubator. That way the horse is born on the moon and grows up in that gravity.
Who are you going to get to gestate the embryo?
I’m assuming that horses on the moon is just part of the plan to eventually get whales on the moon.
Hey we have a lunar colony. We can build an artificial horse uterus.
Shame we never had a chance to put Whitey on the Moon.
It sounds like Heinlein’s The Menace From Earth. Like most of his short stories, I found it quite good, much more so than his novels.
There is a horse rehab center in Ohio that has a long water trough that a horse can walk in that partially supports their weight. I have seen photos of it but it is not featured on this website but I’m not sure it is the same place. Also a giant X ray table where they can lay a horse on its side.
A horse laying on its side in even Earth-surface gravity (gee) for more than a few hours is at risk for organ damage and reperfusion injury. Under launch acceleration of multiple gees (the Space Transportation System a.k.a. “Space Shuttle” had a peak acceleration of ~3 gee) a horse would almost certainly experience internal injury and difficulty of the heart pumping blood efficiently even if it were sedated and fully supported.
Horse chiropractic and acupuncture? 
Stranger
To heck with the nag, how about a kangaroo on the moon?
Horse chiro/body work (mostly facia stuff, various massage modalities) are used a lot and can be very beneficial, as can acupuncture.
With horses you don’t get a placebo effect. They tell you pretty quickly if something has made a difference or not.
And yes, a horse recumbent long term is NOT a good thing.
Can I saddle up a kangaroo? If not, can I ride in the pouch?
That would be…intriguing. A kangaroo actually uses its own weight to load up the legs fora jump; under the reduced gravity that might scale somewhat in proportion but they also use their powerful tails to push forward, so depending on the traction they get they might be propelling forward further than on Earth. Whether they could learn to compensate is an unknown
I would buy you Ko-Fi to see you try that.
Stranger
Considering the logistics and difficulties of getting an animal t the moon and then trying to persuade it to walk there, especially when that’s going to get the in trouble with their expectations, it seems to me that there’s really only one way to proceed.
Bring the animal to the moon while an infant or (even better if you can manage it) while a fetus. That’d require all sorts of advances and inventions, but it might be easier overall. In any event, if you bring an elephant or a horse or a kangaroo to the moon while it’s really young, it will be a lot smaller and easier to transport.
Then it will grow up in lunar gravity. It won’t have to unlearn the experiences of a lifetime. It’ll just have to overcome instinctual behaviors.
If you decide to bring a baby bovine to the moon, you’d have the first “moon-calf”. Shakespeare and .G. Wells would be proud.