Kataphrakts

Kataphrakts were a type of Easterling heavy-cavalry. Their horses were heavily armored and they bore broad shields and curved scimitars. They were notorious for being an incredible defensive force when deployed together, capable of mounting an impressive shield-wall formation despite the fact that they were mounted. They were also an impressive fighting force when used in an offensive capacity, due to the sheer difficulty which enemies had to pierce their armor or to slay their armored horses in order to actually harm the riders.
=== Weaponry and Tactics ===
The main weapon of these heavy cavalry was a long lance-type weapon about 10 feet in length. It was made of ash wood, with a finely wrought and supremely lethal steel head made for punching through plate armor. A full charge by the Kataphrakts was dreaded by the predominately infantry forces of Gondor, who had the most to lose from their feared mounted enemies. The lance could usually defeat enemy cavalrymen (such as the Swan Knights of Dol Amroth) and safely tackle anti-cavalry units (such as halberdiers) with impunity, leaving the sheer kinetic force of the specially bred Rhûnic horses to do the rest.
When the fighting got too close for the lance, a standard-issue scimitar, widely used by the Easterling armed forces, was utilized to continue the battle against the enemies of Rhun (as seen in the depiction above, with the Kataphrakts closing in on a wounded Swan Knight). A Rhûnic long knife may have been used as well, as a last-ditch weapon for self-defense.
=== Countermeasures ===
The Kataphrakts, as stated above, were near immune to melee weapons. This caused considerable alarm among the already stressed military planners of Gondor and Rohan, but fortunately, the few Kataphrakts used in the War of the Ring were too small of a force to make a noticeable difference and were stationed in sectors that left them out of combat, resulting in wasted potential and the elusive wraith of victory departing ever farther from the hand of Sauron.
One possible way to counter them would for a large group of bowmen to fire a volley of arrows at their enemies, hoping for a lucky hit. Should this not achieve its intended effect, the bowmen might retreat to an area where cavalry cannot ride (i.e. dense forest, marshy swampland) and continue their fight there. A mounted cavalry archer force might be able to wear their pursuing enemies out, given enough time and strategic distance; however, no known army in Middle-earth marshaled a cavalry archer force that fought in the War of the Ring.