There is no impact. Cavalry is made differently, you need to forget vanilla. Ancient cavalry didn't had stirrups, they ride without them. They were unable to hit enemy full speed, as such thing would either kill (very pricey) heavy horse, most likely would result in rider falling down, being wounded or even killed in the process. Cavalry charge was purely shock action. Determined Infantry could resist any cavalry unit without any problem, especially elite units like those noble spearmen who can keep heir cohesion up quite well.
for better understanding how cavalry works in R2TR, i suggest you to read this:
http://romanarmy.info/cavalry2_intro/cavalry_intro.html
i will be also posting combat guide very soon, that will explain it in detail, with focus on all possible tactics you can use.
btw, what was experience level of that Noble cavalry, and what was experience of those noble spearmen? I might increase morale penalty for being attacked in rear in next update though.