Explain to him that if horses are truly her passion, then this interest will last much, much longer than soccer and piano will if she's not too fond of them. I did all kinds of sports when I was in lower school, but didn't like any of them enough to stick until I began taking riding lessons. If you want her to stick to a sport, then it needs to be something that she likes. There's no law that says the three of you can't run to the park on weekends to kick a soccer ball around for fun, but she can't really do that with horse riding. The lessons are really the only way into it.
As a kid, my parents forced me to take piano lessons. In fact, I felt rather tricked into it when I was in first grade. My mom asked me if I wanted to do it, and said that I could stop after a year if I didn't like it. After the year passed I said that I wanted to stop, but they made me continue. The reason? My dad took piano lessons a little bit as a child, and stopped. HE regretted not continuing the lessons, and wished that his parents had made him so he could play nowadays. He insisted that we keep with it through high school. Through lower school it was ok, but by middle school most of the other kids had dropped out. My parents told me that I HAD to practice 30 minutes per day, which is probably necessary to really be able to master the music.
By 8th grade I was one of the only students still in the program (it was done through the school) and it was miserable for me. I was busy with (strangely enough) school, horses, and the season of soccer that I randomly decided to sign up for. I HATED piano. HATED it. It was miserable for me, I wouldn't have time to practice, and it was miserable for my piano teacher. Because I wouldn't practice, I wouldn't advance. We'd be going over the same things week after week, and she finally had to contact my parents and convince them to let me quit. I convinced them to let me quit under the condition that I would still play for fun once in awhile, but I didn't touch that piano again for years because of my resentment for it. Playing for fun would have been impossible The better part of 10 years later I've resolved my differences with the piano and will mess around with it for fun with some of my old sheet music. If my parents had let me let it go years earlier, then I probably would have become a better piano player than I am now. That's not really a reason to continue riding lessons per say, but a reason why to not force your child into an activity she's not interested in.
I would try to talk your husband into picking one of his favored activities (soccer or piano), and compromise to save money and time. She gets to do the riding lessons that you want, or the soccer or piano that she wants. Better yet, see if he'll let HER choose between the two. It's not fair for him to control all of her extracurricular activities, and you get no say. To further relieve costs, perhaps suggest that she continue with group lessons instead of individual. Depending on how the group lessons are run, you daughter can benefit greatly from learning from her peers, as well as make lifelong riding buddies. Just make sure it's not your girl shoved into a lesson with 12 other girls that are cantering 3' fences!