Scarlet Royal by Anne Emery (1952)

The only thing in Margo's life that really counted was the horses themselves: riding them, hunting, showing, caring for them, loving them.  Especially her own horse, Scarlet Royal -- hers until the wealthy Cranshaws offered more than the struggling Macintyre's could afford to refuse.  Be nice to the Cranshaws, her mother said.  How could she like Ginevra Cranshaw, who went off with her beloved horse and her best boy friend?

A story of sportsmanship and courage by the author of Senior Year. (from the back cover)