Oy. How much does it cost to own a horse? Start with your paycheck and subtract your rent (or mortgage), food, utility bills, car payment and insurance. Take the remainder and divide by 1. That's how much it costs to have a horse.
The board, the routine farrier, the routine dentist, the twice-yearly visit from the vet for shots are only a starting point. Then you have the lessons for yourself (because owning a horse doesn't mean stopping lessons, if anything, you need them even more because your riding = 100% of the training the horse is getting). Then you have training for the horse, depending on how good you are, and how good the person who is teaching you is, and how smart and not challenging your horse is.
Then you have other stuff, like supplements because your horse is older and needs joint support or your horse is a mare and her hormone swings are making her a PITA or your vet told you that you can't get some of the required nutrients from the hay that is available in your area.
And the saddle fitter/chiropractor/extra trip from the farrier because your horse has suddenly started acting odd when you ride, and you know the first thing you have to rule out is pain from the tack.
And the extra trip from the farrier for the thrown shoe.
And the extra trip from the vet for the weird spots on the nose/possible limp/odd-looking scabby area by the tail/diarrhea/big cut from when the horse rolled over in the paddock and got a foot stuck in the fence/large abrasion from when the horse found the one rock in the entire field and rolled on it/hoof bruise/development of cresty neck and butt fat suggesting a metabolic problem. Don't laugh - everything on this list is something I, someone at my barn, or someone at a nearby barn has had happen in the last year. None of it expected. And none of it, thankfully, really serious, like last year when two of the horses I know colicked and ultimately died from that.
I don't know where you are, OP, but if you're in the north, then you also have the cost of horse clothes (turnout blankets) OR you can go the no-blanket route, but if you do that, I think you usually have to boost the amount of food you're giving the horse. If you go the blanket route, which I do, then there's the cost of the blankets, plus the cost of the blankets you have to buy to replace the original blankets that your horse destroyed playing and fighting with the other horse(s) in the turnout together. Or, if you horse is turned out alone, the blanket your horse destroyed by finding the one sharp rock in the paddock and rolling all over it.
Then there's fly masks, and fly spray - I'm going through 20 oz of that stuff every 10 days or so, and my horse has thin skin and breaks out in hives if I use the cheap stuff, so I have to get my spray from mail order. I go to a place that gives me free shipping, but still, it's quite an outlay.
And there's grooming equipment, and if your horse has dry hooves or dry skin you need something beyond the basic stuff, and there's first-aid supplies because you WILL need those.
If your horse has vices, like cribbing or weaving, you might need extra stuff for that, too.
And the tack, there's tack. The good news about tack is that it's expensive as the dickens, but pretty much it's a one-off. You don't have to buy new saddles and bridles on a regular basis. If your horse already has a bit that they're good with, that helps, because then you just have to get that one bit...otherwise, you might wind up having to buy several bits as you experiment to find one that works well.
Not all horses need all these things, but this is the list of stuff that came IMMEDIATELY to mind when I started thinking about the cost of owning a horse. There is NO question, if you are leasing but not free-leasing, that it is MUCH cheaper to lease than to own. Owning a horse is an incredibly rewarding experience, but in terms of cost, it's a lot like having a kid. The horse WILL suck up your entire disposable income.