I think that trading caravans should actually have carts with them. They could be quite usseful when defending.
They could, for instance, be arranged into a defensive circle which could be defended like a small fort.
Also, there could be archers placed on the roof of a cart, while it was moving or still, which would make not having a horse less detrimental.
I also think that a skirmish command could be quite useful. You could tell mounted archers to skirmish and they would move around without getting close enough to be hit by melee weapons.