I’m assuming you mean for the late Roman empire, as the early Roman empire didn’t use horse armor. Their early cavalry use was as dismount infantry, not light cavalry. As they started to develop their Roman equites corps, it comprised mainly of lightly-armored horsemen bearing spears and swords and using light-cavalry tactics to skirmish before and during battles, and then to pursue retreating enemies after a victory. They relied heavily on their vexilii and auxilii for mounted non-light cavalry (especially Sarmatians).
However, around the 3rd and 4th Century, Emperor Gallienus Augustus and is usurper Emperor Aureolus pushed for there to be Roman Cataphracti (made up of Romans rather than mercenaries), or heavy cavalry, with bronze scale draped over the body and heads of their horses: