OP has already said that they’re not struggling, that this is just “spare” money being used up. Also, has everyone missed that the daughter has a job to help pay costs, and is so committed that this is what she plans to do as a career? I can tell you first-hand that the bond you get with a horse you own and care for every single day is far in excess of that you get from just going to a riding school. It’s equivalent to the bond you get with your dog (I know, we have several of each) – they become your friend, your companion, and sometimes the reason you get up and keep going every day.
You know what, if this were bikes that she were into nobody would bat an eyelid – driving up and down the country to races, costs of race entries, bike maintenance, and so on. It’s because it’s horses and all of the negative connotations that go along with it.
In addition, the OP has stated that because of his historical involment with equestrianism he no longer wants anything to do with that world, nor does he want his daughter to. This isn’t about money at all, this is about his issue with it that he’s taking out on her.
From what has been posted, the daughter seems completely level-headed, adult, responsible, committed, dedicated, hardworking, and the rest – surely these are things that should be fostered and encouraged? If this means not getting to go on a foreign holiday or overpaying the mortgage for a few years whilst supporting the child you chose to have in their desired live, then yeah, suck it up. The OP is acting like a spoiled child because the daughter loves something he doesn’t want her to, and can’t have his fancy holiday. Don’t like it? Don’t have kids.