Now some versions have it-
I'm ridin' old Paint, I'm a-leadin' old Fan; .......

and then-
My hosses ain't hungry, they won't eat your hay;
My wagon is loaded and rollin' away.
*With a pack on old Baldy and ridin' old Dan,
I'm a-goin' to Montan' to throw the hoolihan**.

*Verse variation mentioned in Lomax and Lomax, Cowboy Songs and other Frontier Ballads.

Could be the singer was too drunk to know what he was ridin'.

The whole thing is confused; In the first verse he says "Goodbye, old Paint," and in the second verse he's ridin' him.

**hoolian? The two terms both confused and used interchangably.