An 11th century Norman Knight wouldnt be waring any plate armour he would be in a chainmail suit including a coif.His horse would of had a chainmail chest covering and maybe one for the flanks but in the 11th CE the horse wouldnt have ant face armour,that was much later.The Knights kite shield was designed to protect the riders left side including the leg,thats why its kite shaped,an excellent shield for a rider.The lance's in the 11thCE were basically heavy spears,with this type of lance you can only get the power from the speed of the horse and the riders right arm.The crouched lance (the one with the hand guard) was developed in the 14th CE,this lance is much more powerful as it allows you to get your full body and the weight of the horse behind the blow,much more damaging.
It seems to come down to which is better armour scale or chain? is a scale suit lighter than a chain one? ( i wore a hauberk once and i couldnt believe the weight of the thing) i have no idea,but scale armour looks heavier.
The Norman war horse is a big bugger who's trained to bite and kick the enemy, and he'll allso spin in circles once the Knight has used the lance and is then in the thick of the action.Its spins so it cant get its back legs hamstrung whilst the rider is chopping or bashing the enemy,making it more difficult to bring down.Are the Byzantine horses like this? maybe Tobias knows about Byzantine horses but i havent got a clue .
Pic i found of a less heavily armed cataphract,his horse has no armour.
BTW,high Yoritomo
White robes and a red cross were'nt optional if you were a Knight Templar,thats there orders colours.