That book is called "Chester the Little Pony," and it's not actually a Golden book. It's a Rand McNally Elf book that was published in 1951 and written by Eman Gunder. It was my favourite book as a kid. It was my mom's as a child and she passed it down to me 
The inside cover: http://i61.photobucket.com/albums/h80/dusrob/Scan_Pic0688.jpg
The clothesline: http://www.etsy.com/listing/20775309/vintage-1950s-chester-the-little-pony#zoom
Cassie
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Have been looking for a book about a naughty pony. Runs under clothesline. Cover had a stable with pony heads looking out. This is an old book, probably from late 50's or 60's.