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While the content of this article is based on official information, the actual name of the subject is conjectural, and is yet to or cannot be officially named.
The Siege of the Hornburg occurred during the War between Rohan and Dunland.
The siege began in TA 2758 after the Dunlendings defeated the armies of Rohan, overran their country and conquered Edoras. The populace fled to the dales in White Mountains to escape death or slavery. Their they took refuge while King Helm and a modest group of loyal followers not willing surrender or flee, fled to the Hornburg, a fortress in the White Mountains. There began a deadly siege.
Within the fortification, Helm endured the enemy but the worst was yet to come. The Long Winter that began in November, 2758 brought heavy snows and freezing colds. The terrible weather brought hardship to both sides and there was great hunger to near starvation during the Yule. The hardship and suffering led Háma, the son of Helm to attack the enemy and look for food without the approval of the king. He and his company were lost in the snow. What followed afterward is unclear and possibly part legend but apparently the resistance continued. For it was said that Helm himself grew terrible and fierce during the hardships of the siege. It was said that he continued defending the Hornburg, apparently on just his own dreadful personality with great losses. It was also said or implied that he alone was left to defend the Hornburg, and that he would often go out alone in a mad frenzy apparently without any weapons slaying his enemies with only his bare hands, and seemed nearly unstoppable. Because of this apparent dread, all enemies retreated from the Deeping Coomb. Despite all this, the defenders still perished including Helm.
One day near the end of the winter, the Dunlendings heard his horn but neither he or any of his men appeared. When the sun broke the sky, Helm was found on the dike frozen to death. It is not known if the Dunlendings entered the Hornburg as victors but they probably did not due to the fear of the ghostly terror of Helm's spirit, that had spread amongst them.
Helm's finial stand in the Hornburg led Rohan's enemies to fear ever after the sound of his name and his horn. This fear was used again against Rohan's enemies during the War of the Ring when Saruman's army besieged the Hornburg during the Battle of the Hornburg, when the horn was sounded as a sign of Théoden desire to continue resisting the invaders despite the odds.