The bay was his ex-lover's (and previous victim's) horse. The verse:

"For you can't hang a man for killin' a woman
Who's tryin' to steal your horse."

falls under the same part of Texas culture as the two murders of the preceding medley (track A4 on the album)

Regardless of the exact written Federal, State or Local legalities, the all white male juries would refuse to convict on grounds of temporary insanity (passion) or self defense (broadly known as the Law of Texas)