In the national archaeological musuem in Tehran were a cluster of a dozen or so clay bullae: hanging attachments to a skin or papyrus document which could take a seal. The name is medieval, but the technique is much older. These ones come from the Sasanid period (6th or 7th century CE), and I suspect that they turned up on the art market or in a private collection and the Iranian government was able to show that they had left the country without permission. Several of them show armed men riding armoured horses.
Unfortunately, I had very limited time to take photos of the whole museum, and I do not have a polarizing filter for my camera to reduce glare from the case. The photo above is my best, but I have include several other legible photos below the fold. All are of the same bulla, but there were one or two others with armed men on them which I was not successful in photographing.
The depiction of the horse-armour in bands reminds me of some Tang Dynasty and Sogdian paintings. It probably represents what we call lamellar construction, with small plates fastened in rows and hung from the row above with straps. I am not very familiar with construction of horse armour in those times and places, and would welcome suggestions of surviving pieces with the lacing intact in the comments!
One of the most obvious changes in warfare in the Achaemenid empire is that over time, some cavalry begin to wear more and more armour. In the late sixth and early fifth century, none of the King’s men seems to have worn much more than body armour and a helmet, and perhaps a pair of greaves in areas near the Aegean. Later on, cavalry began to experiment with armour for the neck, arms, and legs and began to put armour on their horses: head-pieces, hanging flaps like oversized chaps, and full bards. This can be seen in monumental sculptures from Anatolia, and in a mix of classical historians and later archaeological finds from the neighbourhood of Sogdiana and Bactria. These more heavily-armed cavalry seem to have fought closer together and come to close quarters more quickly than their counterparts with less protection, and in later periods many of them preferred heavy two-handed lances to a pair of short spears. In Herodotus, Persian cavalry get out of the way before the main battle, while in later historians they sometimes stand and fight against large bodies of enemy troops. So these Sasanid horsemen show a later stage of a process which began in the Achaemenid period and continued long afterwards.
Like their Assyrian and Greco-Roman counterparts, Achaemenid armies usually had ten to twenty footsoldiers for every horseman, and usually placed more footsoldiers than cavalry in their main line. This is very different from Parthian or Sasanid armies, where cavalry were more numerous and less willing to share the glory. The Persians also chose to array their troops in a ‘dense’ way with distinct lines and divisions between units rather than a loosely-formed cloud of soldiers which tried to confuse and mislead the enemy (the Strategikon describes armies from the steppes which arrayed themselves like this, and how they differed from the formations of Persian and Roman armies). Sadly, some descriptions of Achaemenid armies by modern historians owe more to our vague ideas about oriental armies than to the few sources we have. However, by the fourth century BCE armoured men on armoured horses were widely available to Achaemenid kings.
Further Reading: Christopher Tuplin, “All the King’s Horse,” in Garrett Fagan and Matthew Trundle eds., New Perspectives on Ancient Warfare (Brill, 2010) pp. 101-182; Duncan Head, The Achaemenid Persian Army (Montevert Publications: Stockport, 1992); Nicholas Victor Sekunda, The Persian Army, 560-330 B.C. (Osprey, 1992)