Summary Aegon the Conqueror's dream, which he called A Song of Ice and Fire, is revealed in House of the Dragon, a surprising twist that retcons Game of Thrones and reframes the White Walkers' defeat. House of the Dragon's timeline is long before Game of Thrones, some 172 years prior to the Mad King's death and the birth of Daenerys Targaryen. But that doesn't mean there's no impact upon its predecessor.
Aegon's dream is of something that should be familiar to Game of Thrones viewers, because it foretells the coming of the White Walkers and the second Long Night. The terrible winter, the darkness, and the threat that poses a risk to the entire world is a fair summation of the Night King's Army of the Dead, even if it wouldn't come for around 300 years after he had conquered Westeros.
Azor Ahai is said to be a great hero who will wield the burning sword, Lightbringer; the Prince That Was Promised prophecy, which is often changed interchangeably with Azor Ahai, is said to have "a song of ice and fire." Both, tellingly, are rooted in the same idea of the ice and fire duality at the end of the world.
Related A History Of GRRM's Updates On The Winds Of Winter: 10 Key Things He's Said Since Game Of Thrones Started The Winds of Winter is one of the most anticipated novels ever, and George R.R. Martin has given several updates on it through the years. Rhaegar Targaryen, meanwhile, was obsessed with the Prince That Was Promised prophecy; he believed it could be him, and later his son. As the heir to the Mad King, Aerys II, then it's possible he would have been told it by his father . He does speak of the song of ice and fire, though, as Daenerys hears in her House of the Undying visions in Game of Thrones season 2, with him saying:
Is Aegon's Prophecy The Same As The Prince That Was Promised? The Two Prophecies Are Linked As mentioned, there is some overlap in theme and purpose between Aegon's Song of Ice and Fire and the Prince That Was Promised prophecy from Game of Thrones. That's with good reason, as the two are inextricably linked, which was confirmed by House of the Dragon season 1, episode 4.
Although Martin adding Aegon's dream into the books does seem likely, it can't be entirely conflated with the Prince That Was Promised, as Melisandre notes in A Storm of Swords that the savior was prophesied thousands of years ago. Still, it's possible Aegon heard of this, and after his own dream, became convinced the Prince That was Promised would be a Targaryen.