These may be a reach, but they do make reference to horses -

"Love Minus Zero" (Bob Dylan)
"That Song About The Midway" (Joni Mitchell)
"Bonny Light Horseman" (Eliza Carthy & Nancy Kerr)

There's also the famous Stephen Foster song "Camptown Races" - and a little tune from the early 60s that starts out "A horse is a horse, of course, of course ...".