When is it introduced?
This one isn't a prophecy explicitly stated by any religious fanatic or witch, but it's included here because it's a possibly prophetic vision by two different people in two different places at two different times. In season two, Daenerys goes to the House of the Undying in Qarth to retrieve her kidnapped dragons and is shown several visions along the way. One of them is a vision of the throne room in the Red Keep, destroyed and in darkness, and the Iron Throne itself covered in a blanket of snow (although it's important to note that some think the snow is actually ash).
Near the end of season four, Bran Stark travels beyond the Wall and comes across a weirwood tree, which he touches and sees several visions, including — that's right — the thrones room of the Red Keep in ruins and the Iron Throne covered in what appears to be snow.
What does it mean for the future?
As we see in the season six finale, the Maesters send a white raven from the Citadel to Jon and Sansa at Winterfell that confirms Winter has come to Westeros, which could mean a lot of things. Will the Prince That Was Promised never appear, leaving darkness and Winter to take over Westeros, even all the way to King's Landing? Does it mean that Jon Snow will play a role in ruling the Seven Kingdoms? With the Night's King on his way towards the Wall, we'll just have to see . . .
