So I know that we can't expect new significant work on mounted combat mechanics, its still a great system with a lot of details that are too underused. I'd like to see people actually take their horses out into the fields, just suspend disbelief that the horses would never actually get hurt or die.
While mounted, all combat actions uses Outdoorsmanship (which previously included animal lore and horse ownership titles) and Athletics as substitute to Melee Mastery and Defending skill. Likewise, they train the survival skill instead of the usual two combat skills. All combat maneuvers while mounted also trains Tactics as an alternative and reduces the tedium of training tactics on footed combat, but its weighted toward Outdoorsmanship for the horse riding.
In the case of Paladins, they use a blend of conviction and Outdoorsmanship due to their specialized training and so they are not shafted as surivival tert.
Being mounted also offers significant damage boost to LUNGE, CHARGE, and MANEUVER IMPALE attacks.
Being mounted also reduces the effective weight of polearm weapons for the purpose of calculating RT, encouraging it as the favored weapon.
I know there may be concerns that there's already too many skills trainable in combat, but DR is ultimately a combat-oriented game and I feel immersion is more important than mechanics.
Being mounted penalizes ranged single target TM and missile weaponry accuracy, say down to 70% of normal. Thrown weapons have no work around (short of any relevant guild abilities), but Missile Mastery and Scouting and overcome some (not all) of the ranged penalties, say capped to 90%.
For TM, you do not overcome it by skill, but more strategically switch to AoE's or multi-hit spells while mounted to compensate for accuracy loss. (Fireball qualifies as multi hit and is classic for localized AoE)