Here is one for American readers. Photographer Jill Krementz did three books of photographs following gifted children: A Very Young Dancer, A Very Young Gymnast, and A Very Young Rider. This last is remembered with enormous fondness by many of my American friends. The subject of the book, Vivi Malloy, had a charmed and pony-filled childhood, and she was the ultimate in wish-fulfilment.
The book follows Vivi's progress round the American show circuit, and during the course of it, her pony Penny is sold because Vivi's outgrown her. However, Vivi does indeed get the Christmas present thousands upon thousands of horse mad children longed for: a pony. Here she is unwrapping the first element of the present:
You can read more about Jill Krementz and A Very Young Rider here.
Read more about the pony book in Heroines on Horseback, my survey of the world of the pony book from the 1930s onwards. You can buy a signed copy from me (I'll post them worldwide). The book's also available from the usual sources, or your local bookshop.