Pre-gunpowder
The origins of mounted infantry go back to at least the beginnings of organised warfare. With the weight of ancient bronze armour national champions would travel to battle on chariots before dismounting to fight. With the evolution of hoplite warfare, some hoplites would travel to battle on horseback, before again dismounting to take their place in the phalanx. Early pre-Marian Roman military had units consisting of mounted infantry with units clinging to the saddles of the cavalry to take them to battle and then dismounting to fight. The Han Dynasty also extensively used mounted infantry in their campaigns against the Xiongnu confederation. During many of the Han campaigns, the vast majority of the army rode on horseback; either as mounted cavalry or mounted infantry who fought dismounted.
Other notable infantry to use the horse to enhance their mobility include the Genoese crossbowmen, and Viking raiders who would gather all the horses they could find in the vicinity of their landings.
Read more about this topic: Mounted Infantry