Barbara Remington is an American artist better known for her work on J.R.R. Tolkien's books "The Hobbit" and "The Lord Of The Rings" for Ballantine's Books in the early 1960's. https://en.wikipedia.org/wiki/Barbara_Remington
There is no biography available on her apart from a small article on wikipedia but I scanned the small note on the artist printed on this book (below). I just loved the strange animal characters found all over the book as well as the two hairy characters of the story.