Other songs that come to mind.

Widdecombe Fair (Tam Pierce, Tam Pierce, lend me your gray mare)
Which brings to mind The Old Gray Mare Ain't what she used to be.
Old Paint (I ride an old paint and lead an old Dan)
Wild Horse (fiddle tune)
Run for the Roses (Dan Fogelberg)
Pony (Kasey Chambers)
Commanche (Johnny Horton)

Ballad of a Runaway Horse written by Leonard Cohen, sung by Jennifer Warnes & others. Would this one count? May be song alluded to earlier by Emmylou.