I think there's quite a few things that need tweaking to bring Cav into balance with the rest of the game.
1) Ranged Chars should only be able to carry 1 quiver of arrows/bolts/darts/whatever. The ammo in those quivers should then be adjusted to always be the same. For instance, why can someone carry 24 arrows, but only 15 Bodkins which are the same size? Make then both 24 and make that the max (unloomed) arrows that anybody can carry. With scrounging it should be more than enough and will mean HAs stop being the end game annoyance that they currently are.
2) Since HAs now only get 24 arrows (unloomed) I think they would deserve an accuracy boost. However I would couple this with an accuracy nerf for people on stationary horses. This would encouraged HAs to actually try skillful shots whilst on the move instead of encouraging them to continually stop their horses just out of range, fire a few shots and then move away before you can get to them. This has to be one of the most annoying HA tactics ever.
3) Add horses weights to their stats. Then use this and the horse speeds to determine each horses max momentum and base maneuverability on this. Right now I don't think Horses are balanced against each other so it is no wonder some of them are overpowered in the game whilst the average horse is not. So long as whoever picks the weights uses a bit a common sense then it should work out quite well and force Cav to really pick between speed, armour and maneuverability.
4) Add disarms to the game. A Lancer going at full tilt, hitting someobody for a massive amount of damage should have a chance of being disarmed. Link the disarm chance to the damage done when thrusting only and it will make sure this doesn't happen in normal melees and it is only a feature to give Cav something to think about and stop them being able to dominate battlefields doing the same thing over and over again. This would also apply to people stabbing horses that are charging at them, which would nerf 2Handed thrusts vs Cav which are currently OP. Standing directly in the way of a charging horse and thrusting a 2 Handed sword into the horses head (and then into the rider) should not be an preferable anti Cav method. It can be there as a last resort that leads to you being disarmed but nothing more. Since Spear thrusts stop horses rather than damaging them, this will not nerf pikeman against Cav.
5) Nerf 1 handed spear thrust damage from staitionary horses (as suggested by Overdriven). I agree with this suggestion so thought i'd include it in my list
6) Add deployable stakes to the game
Do all that right and I think Cav will end up balanced
EDIT: Completely off topic but this was triggered by what I just wrote so figured I'd post it here. With regards to looming it would be interesting if you could choose how to loom your weapons. For instance, with arrows it would be good if you had to choose either extra arrows or extra damage. With weapons you would choose either speed or damage (or accuracy for bows) and with armour you would choose extra armour or decreased weight. This would lead to a lot more variation in weapons and could be quite good