what was the function of the Roman cavalry?

[Dan Howard]

I think it is possible to train a small minority of horses to charge at an unbroken line of spearmen. I have trouble believing that the majority of any group of horses, regardless of their training would do this.

Regarding attacking the horses, Anna Comnena recounted an incident where the Byzantine commanders ordered the archers to attack the horses of the Franks because arrows were having no effect on Frankish mail armour.