I think stamina would be good, but at this point I'd rather not see it added seeing warband is years old, and m&b even older and they haven't had this since inception.
But to play devil's advocate I had these ideas regarding stamina:
*Infantry doesn't lose stamina from running but it regenerates slower while running versus standing still.
*Infantry loses stamina when they swing their weapon, the heavier the weapon, the higher the drain on stamina.
*Both Strength (getting less tired from the weight of the weapon) along with Weapon Master (learning how to properly swing the weapon) would help negate some of the loss to stamina every swing.
*Horses would have stamina built in where at a medium "trot" they wouldn't lost stamina, but would regain slower than if they were stopped or walking. At their fastest gallop they would start to lose stamina, somewhat similar to Red Dead Redemption.
*Swinging a weapon from horse would drain your stamina similar to being on the ground and swinging a weapon, couching lances would lower your stamina until it was drained, and then your lance would pop up (like it currently does after you couch for 6 seconds or so).
*Holding your weapon chambered would also slowly drain stamina
I'm not sure how to balance ranged with stamina, but it would be similar to melee, when you draw your bow back it would start to lower your stamina, and after say 4 or 5 seconds it would be completely drained and you would have to release the string. It would have to regenerate pretty quickly however if you were stationary, I'd say faster than infantry maybe.
Crossbows seem like they might be OP in this system, but I figure that when they are aiming their crossbow you would start to lose stamina, reloading would also take stamina.