Lt. Brookman
Waterloo disagrees with cavalry being superior.
So does Charge of the Light Brigade.
However, the only problem posed by infantry is when they do that box formation, but even then. Say hello to Tartar's. They out range muskets and reap a terrible terrible mass of life. The infantry have to move, or cannons must be brought to bear.
You also have to remember, a Hill in any fight is always the favoured spot to be. It's horrible to fight against an enemy on the hill.
There's several other things with the Cavalry units must do in order to be amazing, but well controlled in this game the infantry stand no chance.