I have to disagree. Plenty of people from humble backgrounds have horses. Here are some tips.
Choose a horse breed that naturally eats less and also is no bigger than you need him to be. A thoroughbred will eat you into poverty. There is a huge gap in the cost of owning different breeds. A younger horse will have less health issues (until he gets older) but you'll want the stallion to also have calmed down from his boisterous younger years too. I'm guessing 8 years old might be a good number but I'm not super confident on that.
Horse vets are cheaper than dog vets in my area. You can learn to do hoof care work yourself so you don't need to call out a farrier more than a few times to show you how it is done.
It is highly recommended you get your own property to do sexual activities with horses but not everyone does. If you go with someone else's barn, I suggest you go on facebook horse groups / facebook market place / internet searches and look for the cheapest safe-looking barn you can find that allows you to feed and care yourself. It should work out to cheaper per month then the extra property taxes you would pay on buying a horse compatible property. A lot of people in horse-centric areas own houses with small barns in back of them. You might find a place that you rent alone or one other person for a more private experience. If you can find one with a lot of grass then you can pay less for food. Moving to a place with good grass and cheap land with make everything cheaper for you. Tennessee is a good option.
If you get your own property, a real estate agent could give you all the advice I could on being cost effective with that. Location matters (think about Tennessee). Most places are strict on if they allow horses or not, check zoning laws. If you get your own property you can run your own barn to offset your own horse's cost.
You can also rent out an entire barn and then rent out the stalls to other people. You can work at a barn and work out a cheap. You can also negotiate with barn owners to barter for space for your horse by agreeing to do some work at the barn.