Symbaroum handles that scenario abstractly (even the Pitched Battles rules in the GM's Guide doesn't differentiate between troop types - and actually says if you want more detail, make your own system up!!
The horse's speed in melee just isn't considered a factor. The speed of the horse is abstracted down to the fact that the opponent can only take reactions, the rider isn't locked in melee (so no free attacks against him for disengaging) and its going to cost the opponent a Move Action of their own to re-engage (which may require a Quick check or similar, at the GM's discretion).
add more Tactical options to Symbaroum combat (I haven't tried these) by implementing the Movement By Scale rule on p.181 of the core, which requires you to use a combat map/grid and the Maneuvers system from the Advanced Players Guide (that actually has Charge as an option). Not sure these will offer exactly what you're looking for, but it may be a starting point.