I actually have a rather grim hope about this game. It involves two game dynamics that actually existed in the original game:
lasso/hogtie
"Put victim on horse"
In the original game, you could only lay the "victim" across the horse's butt.
Suppose in this game if you could put your "victim" on the saddle of a horse (maybe even yours), and if you find a tree, you can throw the rope over a branch, tie a noose around the guys neck, and even slap the horse's butt to execute the poor you-know-what.
Yes, it's grim. But it might actually also add a GREAT feature to the game - coercion.
Meaning you could also use it as a tactic to get information out of people. Tie them up, put 'em on their horse, string them up, and threaten to swat the horse if they don't talk.
Whether or not you actually DO swat the horse afterward is up to you. And your Honor goes up or down accordingly.
I know it's grim, but hangings were a huge part of the Old West. (especially in the Romantic retellings). Would that not be an awesome feature??