I hated The Horse Whisperer as well! Actually, I really enjoyed all of the parts about the girl and her horse healing and learning to trust each other again after their accident, but the whole adultery/romance plot just ruined it for me, and the ending too was just...blah.
I love horse fiction and have tried just about every book I could find that even vaguely used horses as part of the plot. A few suggestions...
Shadow Horse by Alison Hart - this one is aimed at teens/YA but it's a good mystery that does center on horses. I read it years ago (I was probably 15/16? I'm 30 now...) but only just this year found out that it has a sequel! Which is amazing news as it ends on a bit of a cliffhanger and for all that time I thought that was it!
Horseplay by Judy Renee Singer - this is about a woman going through a divorce who becomes a working student at a dressage barn. It was kind of a comedy and it got weird near the end, but I really appreciated reading about an adult woman. And very horse centric.
The Hearts of Horses by Molly Gloss - I read this one so long ago I don't totally remember plot, but it's about a girl who becomes an apprentice (I think) breaking horses on a ranch during the 1910's. I love historical fiction so I liked this a lot. I think there was a romance plot as part of it.
The Valley of Horses by Jane Auel - This one is a little different. It's part of the Earth's Children series, about very early humans. The main character of this book becomes the first person to bond with and ride a horse. There is so much more to it than that, as it is part of a bigger series, but horses do play a big role in this one.
I think it is harder to find horse fiction aimed at adults because the "horse obsession" that a lot of younger kids have tends to fade out as we get older. And then adults have so much more going on in their lives that a book about an adult rider who is totally wrapped up in getting ready for a big show and drama with the mean girl on an expensive horse (as an example of a super basic plot of many children's/YA horse fiction) is a lot less realistic than an adult rider who rides and shows but also has more complex relationships with others at the barn and in their personal life, has a job outside of the barn, etc.