- Add the hit dice of mount and rider together for the purposes of attack and damage;
- Maybe give a defense bonus to a mounted rider based on the mount's hit dice, too, except against weapons designed to be effective against mounted warriors (like weapons braced for a charge;)
- Adjust attack or defense for various advantages where applicable (height of rider, defender's weapon too short to reach, etc.)
- Without long weapons, attacks on a mounted warrior may randomly strike the mount instead;
- Remember that the rider's attack is separate from the mount's move, so riders can overrun opponents or potentially escape counterattack;
- If running down footmen, make a situation roll (1d6, 5+ means defender knocked down, adjust for relative size;)
- If it's a potentially scary experience, make morale rolls.
I've switched terminology to "mount" instead of "horse", because seriously, why not use it for other things, too, like a wizard riding a golem, or a war elephant, or a pixie mounted on a dragonfly? Ok, for very small mounts and riders, you might need a special rule for the hit dice, since both mount and rider might have less than 1 HD. Use the higher HD as the base HD, convert the other HD to a simple number by subtracting the hit point modifier from 6, add the resulting modifier to the base HD. Example: kobolds (d6/2, or HD 1-3) mounted on giant rats (HD 1-2) would have an effect HD of 1+1.) You can adapt these rules to other things, too, like warriors possessed by the ghosts of their ancestors. Your cleric can use Turn Undead to exorcise possessed creatures, but the effective hit dice is higher than normal...
Ordinary horses don't have to make morale rolls against ordinary opponents (other than snakes) while being ridden; they do have to roll morale in combat if the rider dismounts. Warhorses never check morale against ordinary troops, even when the rider dismounts. Unusual situations or opponents are another matter. Elephants aren't as reliable, but at least they get a bonus to morale for their relative size unless they feel overwhelmed or are seriously wounded. War elephants have a lot of good points to balance out even that unreliability: can carry several archers who all attack at once, overrun attacks are killer, and few weapons can even reach the rider or archers in a howdah.

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