That is, unfortunately, a widespread but major misunderstanding. I can't go into all the details now, but let me just point out that there is a reason that (heavy) cavalry went out of fashion as pikemen took over (very simplified). And where heavy cavalry cannot charge into troops in orderly formation, light cavalry such as the dothraik has no way of doing that to any effect.
A second point is that even in 1v1 combat, it is arguable whether the horserider is at an advantage, especially once the charge is done and you are mostly circling around a particular spot. The person on foot is much more mobile in their movements.