How to beat horse archers in real life?

[Slim_Ghost]

In my games I rely on heavy infantry armored to the teeth such as the elite hoplites or the Roman legionnaires. I order these heavy infantry to stand in front and form a shield wall (or in the legionnaires' case, testudo), while at the same time keeping the flanks checked. I let the horse archers waste their arrows on the sturdy shields of the infantry. After the horse archers used all their arrows they are forced to engage in melee, and thats where I rush in and slaughter them.

Alternatively whenever I invade a nomadic faction I made sure to only engage them in their settlements. They got nowhere to run in those confined spaces. If they chose to run to the outside, that's fine with me. I just capture the town center and hold it until the timer runs out.

Anyway, I was wondering about my first option. Is it a plausible tactic, historically?