Maybe handle it as part of the fiction? Most of the Dark Ages sources that Fallen Empires draws on don't really focus on killing horses, although they do get killed now and then.
Also, need to distinguish between mounted gangs that get off their horses to fight battles, which is most common, and actual cavalry.
EDIT: Hidden in the description for Sword-master is a description of the benefits of fighting from horseback: +1 Harm, +1 armor against non-mounted enemies, mounted enemies get no advantage against you.
I would think those same benefits would apply to mounted gangs fighting against gangs on foot, but who knows? If you do go with this rule, it would be a good idea for it not to apply, or not apply in full, to infantry in defensive positions or shield-walls.
I would probably treat mounted as a tag that can be applied to gangs, and which can be lost if somebody steals their horses or, for example, if they're besieged and forced to eat them all to survive.