Learning to Ride, Hunt and Show (1966) is (as you have probably worked out) not fiction at all. I'm including it because it's illustrated by Sam Savitt and I love his work. Gordon Wright did write a work of fiction (The Winning Streak, publication date unknown), but all I have to go on for the book's plot is a brief summary, I can't tell whether it should be included here or not. As I'm skirting round the subject anyway, I might as well, so here it is:
Daphne Van Allen is not a gracious winner. She thinks she can forget about sportsmanship and still come out on top. She thinks she's behaving perfectly rationally, but she becomes a danger to herself and others. I do wonder just how many unsportsmanlike riders Gordon Wright saw in his career, and whether anyone ever recognised anything of themselves in Daphne Van Allen.
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More on Gordon Wright
The National Horse Show