There are a few of us (I'm currently horseless, but will be reacquiring soon). Horsepoor and J Mo are two of the others I can think of. It's not exactly a Mustachian expense, but doesn't have to be horrifically expensive. Personally, I find life with horses to be so dramatically better than life without horses that I'd rather spend the money on it than be FIRE. The truth with horses though is you either pay in time or money.
I used to keep 2 horses very inexpensively. I had low-maintenance horses and did self-care board at a backyard barn with a lot of pasture. My total board was $250/mo, and then the owners offered me board discounts for doing some of the barn work and watching the farm when they went on vacation. Neither needed shoes, and I trimmed their hooves myself. Until later, when we ran into health issues, they ate only grass in the summer, and only hay in the winter. They lived outside with a shed, so no stall cleaning to do or shavings to buy. I gave most of my vaccines myself, and most years only had one vet visit per horse. I'd buy a round bale of hay at a time from a nearby farmer, then supplement it with better quality hay. I took lessons when I could, but mostly opted for trail riding and inexpensive competitions like competitive trail, hunter paces, and local fun shows ($10 or less per class). I traded for some of my lessons by doing barn work and grooming for shows. I bought inexpensive trailers twice, fixed them, sold them for a profit, and was finally able to buy a nicer one. I owned an older truck, but used a Neon as my daily driver. I mixed my own feed and bought generic supplements when it came time for that. I got a part-time weekend job at the vet practice that I used and got an employee discount.
Of course not all of those work for every horse owner. I was single, no kids, so part time jobs and daily barn trips were completely reasonable. Right now we own land, and though we're moving soon we're looking for land again. That's the most reasonable way for me to keep horses inexpensively now.