Where are the Horse Stories?
A classic author is Marguerite Henry who wrote Justin Morgan Had A Horse and Misty Of Chincoteague, and more based on true stories.
For easier reading levels, try books on ponies in the
Animal Ark series like Pony At The Point; and the
The Pony Pals series with A Pony For Keeps.

For more difficult reading, try the
Lucky Foot Stable series including Lady's Big Surprise, or the
Heartland series with After The Storm and many more.