Horse armor (barding) was apparently developed extensively in the ancient world. It was used by the feared cataphracts of the Sassanids, and later also Greek cataphracts.
So if barding was so common in the East for such a long time, why wasn’t it common in medieval Europe?
I know it became common in the late Middle Ages, but I haven’t seen any sources showing the normans or other European heavy cavalry of the early/high Middle Ages using barding in any form.
There is definitely depictions and mention of barding of horses int he high medieval era. This manuscript from 1250 http://manuscriptminiatures.com/4974/15409/ shows some as well as the Kings mirror circa 1250 "He should also should have a good shabrack (14) made like a gambison of soft and thoroughly blackened linen cloth, for this is good protection against all kinds of weapons. It may be decorated as one likes, and over the shabrack there should be a good harness of mail." These are some of the first references i have seen to barding but still fall just within the high medieval period. The reason for the late adoption of barding is probably due to cost and weight. It would take a very large amount of maille to competently cover a horse. you also need to remember that adoption of maille leg armour was only starting to become common on humans in the late 12th century.