Barbara Willard (1909-1994) is not really a ponybook author; the inhabitants of Ghylls Hatch in her excellent Mantlemass series are horse breeders (at least in the earlier books), but the action is definitely not horse-centred. That said, this is an extraordinarily good historical series, and I can heartily recommend it.
Her one just-about pony book is The Penny Pony (1961), in which two small children who can’t afford the real thing earn a penny to buy a life size model. It’s a charming read, aimed at younger children, in which Cathy in particular has to accept that losing one thing might well bring something better.
Barbara Willard was educated at a convent school, and tried acting before settling down to writing: her father was the Shakespearian actor Edmund Willard. Her first adult book was published when she was 22, and she wrote a book a year until the outbreak of war in 1939. When the war ended, she went to live in Sussex, the setting for the Mantlemass novels. She went on to write over 40 novels for children, winning the Guardian Award for The Iron Lily in 1974.
Finding the book
The Penny Pony is easy and cheap to source in all its printings.