Oooh... all the Pullein-Thompson books are wonderful, my favourites (still in the pile by my bed, and I'm over 60!) are Riding With The Lyntons, Three Ponies and Shannan, and Phantom Horse. Ruby Ferguson's 'Jill' books are lovely, but the language is even more old-fashioned than the P-T sisters' books.
Sheila Chapman's book A Pony and His Partner is my favourite ever. The Jinny books by Patricia Leitch, the series starting with For Love of A Horse, are fabulous and more recent. Ruby Ferguson's 'Jill' books, starting with Jill's Gymkhana, are lovely but the language is even more old-fashioned than the P-T sisters' books. It's quaint, 1950s, very correct!
Monica Edwards wrote some great stories, and I have a gorgeous book by Monica Dickens called Talking of Horses, a collection of musings and memories of her own life with ponies and horses, it's lovely. Black Beauty, of course, guaranteed tear-jerker. The Silver Brumby books, set in Australia, are brilliant. Ride a Cock Horse by Elma M Williams is an account of her life with ponies, not fiction, a delightful read. Saddle Club are a really fun series but American, my daughter loved them. Follyfoot....
Hope you find something suitable OP, sorry my list is full of my own memories!