Horse armor in general was more of an Eastern-European/Eurasian thing. Any horse armor in the west was considered "heavy" and the typical armor used was simple padding or just a heraldic sheet.
It's a mistake to call Knights, at least in their early/high iterations, as heavy cavalry. That belonged to the Romans and their Cataphracts which were armored like tanks and would briskly trot into the enemy, beating them over the head with mauls or impaling them on lances (which weren't so much used for couched charges as thrusting).
Meanwhile the Knight was specifically shock cavalry. Their horses were fast and they were supposed to slam into an enemy unit and then either run down the broken remnants, or retreat and form up for another charge if they didn't break.