Jose gives a useful account of heavy armoured cavalry in our world,
but leaves out one type. The first such cavalry in Roman service
(and this is in the Western empire) were Sarmatian auxiliaries
from the steppes, who served using their native equipment.
This included mail armour for both horse and man, kontos and bow.
I'm not aware of evidence whether they had stirrups, but they were
serving in Britain earlier than Adrianople,. which is often
stated to be the first appearance of heavy cavalry with stirrups.
Andrew