As for mounted combat - historically, mounted warriors are strong en masse. Yes, when you're fighting a war, a line of armored men on horses at full gallop were a power to be reckoned with.
However, D&D does not focus on mass combat. D&D is about small unit tactics. There, horses aren't nearly as powerful. A footman in a formation can't dodge a line of lancers. A fighter in a field facing one horse has only to wait until the last moment, and take a step aside. In D&D combat, human agility over very short distances tends to win over a horse's mass and longer-distance speed.
So, if and when we have mass combat rules for D&D, I would expect the strength of cavalry to be included. But for D&D's skirmish-scale stuff, I don't know if it is really an omission.