Cavalry in Period
Before the 10th century, mounted cavalry were unusual on the battlefield, as the stirrup had not been invented, and mounted combat less effective. Pitched battles would largely have been fought by infantry who may have ridden to the field, then dismounted on fought on foot. After the stirrup gained widespread use, however, cavalry became dominant on the battlefield.
In the latter part of the medieval period, most noble warriors would have fought as cavalry whenever possible. The word cavalry shares the same root as chivalry, and implies a better social standing than a common foot soldier.
Cavalrymen were expensive, difficult to train, and hard to supply. They were also the primary form of full-time medieval soldier, as anyone who could afford a the accoutrements of the cavalry also had the time and income to train in their use.
A warrior who owned his own horse, armour and weapons and possessed the skill to use them was a very rich man, and could support himself for life. Knighthood in period was less about nobility and chivalry than about possessing the skills to fight from horseback.
Cavalry in the SCA
The serious risk to life and limb involved in learning medieval mounted combat means that mounted combat in the SCA is forbidden. While some SCA events do have horses present, only rarely will they be used to demonstrate even the least dangerous skills involved in being a cavalryman (such as tilting for rings) and never used during combat.