Mary Oldham

Possibly a British author. I know nothing about this author except that she wrote two pony stories, one for young adults and the other a rather unusual story about a plump girl trying to lose weight! The latter,
The White Pony, was not published in the UK, only in America.

Horse and Pony Books

A DREAM OF HORSES
aka A HORSE FOR HER (USA title)
(HARRAP 1968)
ILLUSTRATED BY ROBERT HODGSON
Reprinted in the USA by Hastings House in 1969 under the title
A Horse for Her
EDITIONS PICTURED: 1st edition, USA edition with new title.
SUMMARY: A horse mad librarian finally achieves her dream of owning her own horse.

THE WHITE PONY
(HASTINGS HOUSE [USA] 1981)
SUMMARY: Can Barbara's beloved pony, the old blind white mare Bianca, give her the inspiration to lose weight and please her parents?

Collectors info:
The White Pony was never actually published in the UK and so is hard to find here. It is quite easily found in America though, and usually low cost. A Dream of Horses is conversely easier to find in the UK. It is not common but can be found on internet booksites for a reasonable price. The American version under the alternative title is also not too hard to track down.