I haven’t found any definite information about the author (yet), save for the tantalising fact that Mary O’Hara, of My Friend Flicka fame, had a father with that name. The author on this page of course could be someone else entirely.
Finding the books:the Paul Brown illustrations makes the books expensive. George and his Horse, Bill, is the easier of the two to find.
Links and sources
Terri Wear: Horse Stories - An Annotated Bibliography
George and His Horse, Bill
Dodd Mead, New York, 1948, 164 pp, illus Paul Brown
Bill the horse was to be sold at auction. He’s not a pretty horse, as even George, who falls in love with him, has to admit. However he looks, Bill has many sterling qualities. He is gentle and brave, and just the right horse for George, who has been ill, and is not allowed to do much. However, he hasn’t actually been told he can’t ride Bill, so ride him he does, but in secret.