Based off a long conversation from Twitter, but I’ve started to have some ideas about the Horn of Joramun, one of the more significant objects in the series if assumptions are right that it will bring down the Wall.

The Horn is a curious object, because it seems to have a strong duality about it: it’s known as both the Horn of Winter and the Horn of Joramun, and it is supposed to have "woke giants from the earth” and it’s also supposed to have the power “bring this cold thing down.” And yet, even through Joramun was a King Beyond-the-Wall “in ancient days,” whom Jeor Mormont places as coming before the Horned Lord and the brothers Gendel and Gorne, and describes all of them as having “broke his strength on the Wall, or was broken by the power of Winterfell on the far side,” the Wall still stands.
Why did Joramun never use the Horn to bring down the Wall?
The answer, I think, lies in the other thing we know about Joramun – his involvement in the legend of the Night’s King (the real one, not the one from the show):
“He brought her back to the Nightfort and proclaimed her a queen and himself her king, and with strange sorceries he bound his Sworn Brothers to his will. For thirteen years they had ruled, Night’s King and his corpse queen, till finally the Stark of Winterfell and Joramun of the wildlings had joined to free the Watch from bondage. After his fall, when it was found he had been sacrificing to the Others, all records of Night’s King had been destroyed, his very name forbidden.”
This cooperation between a wildling King and a Stark of Winterfell is unprecedented, which further emphasizes that the Night’s King was an abomination (binding “his Sworn Brothers to his will” with “strange sorceries” should be a hint) rather than some sort of marriage alliance to cement an imagined Pact between White Walkers and humans (which theory constantly ignores that the wildlings have always been living north of the Wall). It certainly demonstrates that Joramun clearly viewed the White Walkers as an existential threat so great that it involved allying with one ancient enemy (the Starks) to free another ancient enemy (the Night’s Watch) from sorcerous bondage.
Here’s what I think happened: Joramun was an early King-beyond-the-Wall who “broke his strength” on the Wall and, looking for a solution to this strategic problem as so many KbtW did, turned to magic. Specifically, he created a horn which was imbued with the magic of giants, which could both wake them from their slumber (perhaps giants are prone to hibernation?) and bring down the Wall. On a sidenote, it’s possible that these two things are linked, if GRRM is a fan of Attack on Titan and has giants walled up inside the Wall whose awakening would shake it down from the foundations. (Just laying down a marker in advance of TWOW…)

Regardless of how the thing worked, Joramun was interrupted by the crisis of the Night’s King before he could bring down the Wall. And what he saw and experienced in fighting the Night’s King convinced him that the White Walkers were such an existential threat that the Wall had to remain to keep humanity protected, even if that meant his own people had to remain in exile. (Perhaps this lesson is why the Horned Lord had his maxim that “sorcery is a sword without a hilt. There is no safe way to grasp it.“) And so he had the Horn buried with him to keep it from ever being used.
To me, this version of events works on a number of levels: it reconciles both aspects of Joramun’s history, it explains why the Horn has never been used before, and it fits the “human heart at war with itself” model of GRRM’s writing, as Joramun is caught between his love for his people and his humanity