As for how mounts might mechanically be implemented, I'd suggest giving a static bonus to attack and defense while mounted. Ideally, this would be negated against other mounted opponents, but this might be too tricky to code. Obviously, one of the major bonuses of mounts would be as a means of faster and safer travel, which means they should be fairly pricey.
Of course, other sufficiently wealthy factions might also have mounted squads roaming about... if you manage to take one off a slain opponent (I suggest making mounts run away in a panic if their rider gets dismounted in a fight), a sort of "taming" system might need to be implemented, since one of the major gameplay nuances of Kenshi is the struggle against the dangers of the environment in your travels. Mounts should never come easy.
Onto the actual ideas I got from mehelsel's comment: Stables. A stable makes for another useful building, and more of those are always nice to have, right?
Finally, there should perhaps be a Riding skill. How it would be implemented, I'm not certain... Perhaps different mounts (of different species, hopefully?) would require a certain Riding value in order to ride, or maybe it affects the riding speed of the mount or your combat ability while mounted (you start at a penalty, working your way up to a bonus as you reach high Riding level). A small beast of burden akin to a burrow would require no Riding skill, which would make it good for training on. Alternately, a sort of "mechanical horse" contraption might be implemented to train the Riding skill.
Just my thoughts. I hope it's alright that I made a new thread for them, since I do know others have already mentioned mounts to some degree.