The Assyrians were one of the first major powers of Ancient times to incorporate large numbers of Cavalry into their army. Over time, they started to replace the more traditional Chariots. The Assyrian Cavalry included archers and spearmen ("lancers"), both light and heavy; the heavy cavalry in particular may well have been dual armed with both.
Assyrian Heavy cavalry Horse Archers
As noted above, they may have carried spears as well. The torso armor was the same "mail" of small plates of iron sewn together into a short sleeved shirt of armor seen on their infantry.
As with the rest of the army, the cavalry units nominally belong to a certain "Division" depending upon the color of their tunics; these Cavalry wear the light orange of Division Shamash.
A second unit of (Minifigs 25mm) Assyrian Heavy Horse archers.
The units have sub units of 2 stands each, distinguished by their own color to the fringes, etc, in this case, one red and the other white.
The light purple tunics indicate that these fellows belong to Division Nergal.
Assyrian Light Horse archers
Presumably they performed the scouting, harassing, screening and raiding functions that would characterize Light Cavalry for the next 1,000 years!
The green tunics place them in Division Ishtar.
Assyrian Horse archers are seen in this bas-relief; an effective saddle had not yet been invented; stirrups would also come much later in Ancient history.