Suppose a horseman's mount was killed in combat. I assume the cavalryman would break away from battle lines and return to camp sans horse, right? What would happen after that? This question pertains to no particular historical period, simply whichever you are most familiar with.
Typically, cavalry, as the general elites of most medieval armies, rode to battle with multiple horses. Many of the Byzantine military manuals, such as the Taktika of Leo VI, advise that the cavalry regiments supply at least two horses per man in case their first mount was killed. These soldiers, if dismounted, were to find their way to the reserve, or rearguard, where they would be given their second horse and allowed the resume the fight, assuming they weren't injured.