Chestnut Mare by Roger McGuinn and Jacques Levy

Always alone, never with a herd
Prettiest mare I've ever seen, you'll have to take my word

And another vote for Doney Gal from Cowboy Songs by John Lomax

A cowboy's life is a weary thing
Rope and brand and ride and sing
Yes, day or night in the sleet and hail
He'll stay with the dogies out on the trail

Rain or shine, sleet or snow
Me and my Doney Gal are bound to go
Rain or shine, sleet or snow
Me and my Doney Gal are bound to go