Conquest of Arnor
Many years ago, the Kingdom of Arnor in the north had split into three different realms. Cardolan, which bordered along the Barrow-downs. Rhudaur, which lay just below Angmar. Finally, Arthedain was the largest realm, governed from its capital city, Fornost.
The Witch-king intended to conquer the three realms by destroying all the Dúnedain and their cities. Rhudaur was the first to fall, and Cardolan was the second. Finally, the Men of Carn Dûm attacked the realm of Arthedain and the city of Fornost. They destroyed the last north kingdom in TA 1974.
A year later, a large force arrived from Gondor, and allied with the Men of Arthedain and the Elves they routed the Witch-king's army at the Battle of Fornost. The war destroyed the Men of Carn Dûm and the kingdom of Angmar. Afterwards the Witch-king abandoned his realm, and retreated south to dwell in his new stronghold Minas Morgul.
Portrayal in adaptations
The Lord of the Rings: War in the North
Despite their supposed destruction, in the video game The Lord of the Rings: War in the North the Men of Carn Dûm were not all slain. Those who survived returned to fight for Sauron under his deadliest servant Agandaûr during the War of the Ring. They are first seen standing on either side of Agandaûr at Sarn Ford after the Nazgûl have pillaged it.
They are seen more often after Agandaûr meets and tries to convince the dragon, Úrgost of the Grey Mountains to serve him. Agandaûr leaves the Men of Carn Dûm behind at the dragon's lair to stand watch and await the dragon's answer. They soon take part in Agandaûr's attack on Nordinbad, in which they fail due to Eradan, Farin, and Andriel intervening.
After their failed attack on Nordinbad, they battle the trio who have come to destroy Agandaûr at their ironclad Fortress of Carn Dûm itself. When Agandaûr is destroyed at the same time as Sauron's destruction, the Men of Carn Dûm are scattered. Those who still lived may have fled the stronghold, or were picked off by the dragon Úrgost who - sensing Sauron's destruction - claimed it for himself.
The Men of Carn Dûm have the appearance of a barbarian. Their beards are long and bushy, they're very muscular, and have very savage fighting styles. Their helmets have horns on them; they wear wooly armor, and wield large weaponry such as hammers, maces or axes.