I haven't worked with horses since I was growing up but we had several breeds. We didn't ride them very often and they roamed most of a 100 acre farm with hills, woods, pastures, rocky hills, etc..
We only had their hooves trimmed once in all the years we raised them. They never saw a vet. They were quite healthy. The only horses that had previously been on the property were a couple teams of draft horses that were stalled and worked.
I just went on the LongMeadow Ranch website this morning. It is a local rescue ranch operated by the Humane Society for all things not dogs, cats or cage birds.
They have sheep, goats, chickens, turkeys, cattle, hogs, guinea pigs, hamsters, llamas, etc. However, the disturbingly vast majority of animals up for adoption are horses and donkeys. They probably have at least 50 horses available.
That's partly because horses are expensive to maintain if you don't have just the right conditions and just the right horse. The right hooves, on the right terrain, can be self-maintaining, but that's often not the case. We have soft, sandy soils here, so hooves overgrow if they aren't trimmed every six weeks or so. Eventually, they start to self-trim, but you can't be sure just where the chunks will break off, so they look like the dickens and the horse may be periodically lame if a chunk breaks back far enough to make the foot sore.
I have a horse that has very thin soles on her feet, who also manages to find things to step on and make holes in them. She was lame again last week - the only thing I can think of that did the damage I saw to the sole of her foot was a piece of stick or tree root. In the grand scheme of things, this animal would not last long in the wild; she is one of those that simply must be wormed on a regular basis. If she were left to roam on a hundred acres, she would eventually be found dead or near death in some remote corner . . .

I think another reason that equines are over-represented in the rescue is because they exist in a sort of no-man's-land between the categories of "pet" and "livestock." Most people who get the other animals listed know they are farm animals, and are at least prepared for them to be dealt with as such. But there is a sort of romantic attitude about horses, and a lot of the people who get them really aren't prepared for the realities of a horse, whether it be the physical needs of the animals or just what interaction with them is really like.
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