A fine tactic, that "The cavalry buttrush" of yours, but I never have enough mounted troops to have a 3x cavalry superiority over those fullstacks of nomad horse-archers.

What I am currently doing with the Sauromatae in my Romani campaign, is hiring the Bosphoran Heavy Archers to face their HAs and Hoplitai (Greek Classical Hoplites) to finish them off, especially to finish off that heavy cavalryand bodyguards the Sauromatae have. I also have a couple of Cohortes Reformata to deal with their infantry and to hopefully soak up some missiles while in testudo formation. (Although I've noticed AI is smart enough not to attack high-armour units with missiles, when it knows it cannot damage that unit - the AI only attacks the medium and lighter armoured men). So I basically have no cavalry of my own, save for a general's bodyguard and a unit of Thracian auxilia.

BTW, it is really annoying (but historically accurate) how every nomadic mounted unit has a bow in addition to a lance.