2h cavalry is impractical from many standpoints.

for example:

A. Your defenseless on the side you aren't swinging your sword, making you an easy stabbing dummy by spears.

B. It's very cumbersome using a 2h weapon while being atop a horse, especially since you can't put your weight into the blow effectively.

C. 2h weapons are usually used to overpower your foes with excessive force, to crush their armor and shields through sheer might, and if your cavalry, it would be easier to either let the horse do that (just by kicking or bumping into people) or to merely charge with a lance or similar weapon which has an even greater shock(both physical and morale) effect upon the enemy.

of course, i'm only using my logic to dictate this, but i think it has some good points to consider regarding this