Got this info on-line that connects Stewball and Molly and Tenbrooks:

Skewball: The Ballads

In America, the Stewball ballad was "...most popular in the Negro south, where the winning horse is known variously as 'Stewball' or 'Kimball," and was apparently one of the chain-gang songs. The song was recorded by Leadbelly in 1940 (cd available via the Smithsonian Museum), by Joan Baez (album title Joan Baez/5), and by Peter Paul and Mary.

There is a closely-related American song, called Molly and Tenbrooks (also Run, Molly, Run), which celebrates the famous and controversial four-mile Kentucky match between the mare Miss Mollie McCarthy and Ten Broeck in 1787. There are several versions of this song, as well, and Folklorist D.K. Wilgus believed there was a connection between the Skewball ballad and Molly and Tenbrooks. In the real race, which Ten Broeck won, Mollie staggered and was distanced in the first (and final) heat, an incident seen in the Baez version of Stewball.

Below are two of the five versions of Skewball from the Bodleian ballad broadsides; the one on the right is dated 1784, the one on the left undated, but it appears to be the older of the two. To show how lyrics change over time, the Steeleye Span version of Skewball (from Ten Man Mop or Mr. Reservoir Butler Rides Again, available on cd from Shanachie Records Corp. (© 1989)) and the version (Stewball) sung by Joan Baez on the album Joan Baez/5 (Vanguard: VSD-79160), the latter set to a tune by the Greenbriar Boys.

-Richie