Perhaps it's because the vast majority of pony books published in the UK were not aimed at the younger reader. When the British reader thinks about pony books, it's the teenager you think of: the Jills and Jackies, the Pullein-Thompson oeuvre, not a book aimed at someone only just beginning to read. In America, they did things differently, and there's a whole wealth of pony books for the younger reader. They're illustrated by artists like Paul Brown (the uber-equestrian illustrator in the US - his books are spectacularly expensive) and CW Anderson. Both these authors wrote, and illustrated, for readers over the whole age range.
Billy and Blaze (1936) was the first of a series featuring Billy, and his pony Blaze, in which together they get lost, and tackle fire, flood and other disasters. In the first book, Billy is the classic child who wants a pony but doesn't have one. He gets to ride the farmer's workhorse, and when he does, imagines it's a prancing pony. Did you ever dream that one day your parents would say to you "Go outside, because there's a pony in the garden?" Because that is pretty much what happens to Billy.
Billy's world is one in which there is no tyranny of riding equipment. Like the rather later Jill in Ruby Ferguson's books, Billy rides in shorts and a shirt, though he does always, always, wear a tie. Even when he enters the horse show, he's still wearing his shorts. Perhaps CW Anderson was making a point. One of the illustrations shows a man in correct riding kit, with a horse strapped down with martingale, strong bit and hood, kicking his way through a fence. Billy doesn't do this - he clears the fences, and what's more he clears them with his pet dog by his side too. And they're awarded a silver cup.
This book was the first CW Anderson published, and it's fair to say he was still finding his feet as an artist. Despite this, the illustrations have a unique charm, and the story has an almost spectacular innocence: it's just a boy, his pony, his dog, and a general sense that all's right with the world.
Billy and Blaze was first published by Macmillan in America in 1936. It was reprinted several times, and is still in print, as well as being available as an ebook. I have to say that the ebook can in no way supersede the actual book.
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For more on C W Anderson, including illustrations of most of the horse books he illustrated, see his page on my website.