The best candidate for authorship of "The Last Longhorn" is John Wesley. According to Johnny Kendrick, Wesley was a Civil War veteran who settled at Pease City, Texas. c. 1880. He wrote several poems, which appeared in local papers. Kendrick says Wesley wrote the poem in 1889 for a "Saturday Night literary meeting."
Carl Sprague's 1930s recording is mentioned by Kendrick.

Jim Bob Tinsley says the song was popularized by R. Walker Hall of Vernon, Texas, a jurist and western versifier, who printed the song in 1916 in "The Cattleman," with the title "The Passing of the Old-time Cowboy and the Last Longhorn," author John Wesley. Eleven years later he published under the title "The Last Longhorn," no author cited.
Charles Siringo published the poem as "The Tough Longhorn" in his booklet of cow-camp poetry.

In 1921, Jack Thorp said he was unable to trace the authorship.

Lomax, in the 1938 edition of "Cowboy Songs ...," said the song was "said to have been written by Judge R. W. Hall of Amarillo, Texas."
Most of the above from Last Longhorn
--------------------------------

The longhorns in "Lonesome Dove" came from an Alberta Ranch which also, I believe, furnishes horses for rodeos.

As a graduate of Texas University, I have to mention "Bevo," their longhorn mascot, which is forced to watch football games when the team plays. He is Bevo Roman numeral something or other; there have been a succession of them.