Assuming an infantry and cavalry player of equal skill fight 1v1, if the cav loses his horse he IS boned, since some of his skill investments are worthless. Your suggestion is already in place. Cav isn't OP, their mobility just lets them pick off peasants and bad players before infantry and archers can even see the enemy.
Man is it fun getting 3-5 kills and not dieing on a foggy plains scene. With 1,400g of upkeep and no heirlooms. But hey there are other levels where using a horse is a terrible idea, so I feel that it is fairly balanced.