Predictions for the end?
At the Citadel, Sam finds that the Maesters are working with a new substance called "coal". A Grandmaester has created the first steam engine. Eventually this is used to power mechanized armor suits and airships.
The Others are defeated halfway through TWoW when Bran sacrifices his body to spirit bomb them with the power of love. Inspired by this sacrifice, Stannis puts aside his claim to the throne and takes the black, and is soon elected Lord Commander of the Night's Watch.
Arya dies in a shipwreck on the way back from Braavos. Jon has been dead since the end of ADWD. No warging, no resurrection. He's gone. His death is mentioned once in an early Winds chapter, and he is never spoken of again. Sansa comes to love Littlefinger. They have a son named Robb. Undead Catelyn rediscovers her love of life as a grandmother.
Bob Strong stands for the throne in Cersei's trial by combat, but he is defeated by Lancel Lannister. Cersei is unceremoniously executed.
Drogon toasts Victarion's fleet in the first chapter of Winds. The Greyjoys are never heard from again. Dany easily defeats the armies outside Mereen and falls in love with Tyrion. Tyrion and Dany get married and jointly claim the Iron Throne. They then relinquish the monarchy and establish a democratic republic. Sandor Clegane is elected as the first President.
Along with Hodor, Tyrion and Dany ride off on the three dragons. The series ends with sunset.jpg
No one knows what happens to Rickon.