|Henry VIII's horse armour from the Tower of London.|
The foundation of cavalry attacks is the concept of shock tactics. A cavalry charge was designed to break an enemy's cohesion and force the units to route. The attack was as much psychological as it was physical. A routed enemy could then be more easily mopped up and would yield the battlefield. In D&D combat, a charge only grants the attacker some bonus to hit and/or damage and maybe a malus to armor class, depending on your particular flavor of rule sets. Conversly, set pikes can do double damage to a charging opponent. Overall, these mechanics are pretty useless in terms of D&D combat and they rarely ever see the light of day especially in a dungeoneering setting. So let's focus on the concept of shock attack.
A charge on horseback forces a morale check on the receiving end. A failed morale check causes the enemy to break formation in some fashion. The greater the failure, the worse the effect up to a total route forcing the enemy to retreat in disarray.
Conversely, pikes would force an opposed morale check between both cavalry and pikemen. Three different results can adjudicate the end effect. A success for the cavalry and failure for the pikemen results in a route as above. A failure for the cavalry against a success for the pikemen results in the cavalry force being disarrayed while the pikemen retain their cohesion. The cavalry would be vulnerable to a follow up melee exchange and would require a good bit of rallying before they could reform ranks for another charge. A pair of failed results would result in both units losing cohesion with the cavalry unable to follow up in melee and the pikemen being unable to maintain a coherent line.
This could be scaled down to even D&D proportions: a single horseman could charge against a single enemy to force a morale check. Would be an interesting mechanic that adds another dimension to D&D combat.
Perhaps in a follow up post the mechanics could be sufficiently derived.