I'm really tired of this short sighted differentiation between calvary and infantry, not to mention they have totally forgotten the use of chariots in ancient Chinese battles (South pointing Chariot is just a toy to MC) which should be useful in this World Online.
There is such a thing as mobile or mounted infantry meaning that you put them on horses or in chariots and they can move in conjunction with calvary units therefore maintaining similar speeds. Upon reaching the battlefields, they dismount and form up their regular infantry/archer units while engaged in war. All it takes is using your horses wisely...
LazyLisy