Did not participate in this discussion before....
Bran is in position to wield power... either save the world or condemn it. As sweet of a boy as he was, he's falling into the same path as Joffrey, Dany, Jon, and every other child/teen in GRRM's mind. Given great power, Bran lacks real experience and a moral compass to apply this power fairly. While not being a sadist like Joffrey, he'll respond emotionally like Dany.... not that this is a quality only for children. Though highly intelligent, Catelyn and Tyrion both act much more on emotions than reason. I can imagine Bran doing some horrible things.... like performing genocide upon the Wildlings, the Maesters, Lannisters, or Boltons. Anyway, I can see Bran saving the world like Tyrion saved KL... by killing men in their thousands.
Rickon will die. Mayhaps like in the show, but GRRM will not let the Starks survive in the male line. Shaggy may survive to terrorize the North.
Arya will not survive either. She's a liability to everyone, even the House of Black and White. Undoutedly, Arya will kill many people. I think her arc will show her experience in not using her power to kill men like Weese and Chiswyck (even though they're on her list), but to deal with the people who affect entire nations like Oberyn, Varys, Middlefinger, Euron, and Cersei. Yes, I know that Cersei is prophesied to die by the valonqar, but that doesn't mean Arya won't come for her... she's on the list.... but the valonqar will beat Arya to it or Arya will be diverted to someone else.
Robb.... yes, I know Robb is dead. Robb's memory will live in the memory of the North for a long time. Robb and Jon idolized Daeron I, the Young Dragon, and Robb's story mirrored Daeron's. Robb was the first Stark in three hundred years to style himself a King. His memory will be an inspiration for family, glory, and love to those looking for those things.... and he'll be remembered as a fool, a cautionary tale to the patient, the planners, and the elderly.
Jon.... I've gone back and forth over the years regarding Jon's father. Eddard, Rhaegar, or Aerys II seem the three possible candidates to me. Even if Eddard is his father, he is still a Snow... unless Robb legitimized him AND somehow this treasonous act by a traitor is recognized by the Iron Throne OR if the North is permanently partitioned from the rule in KL. Anyway, Jon is in a bad position at the end of ADWD. He'll be alive somehow further in the story... but I see his story as being the story of the Wall and it's connection to The Other. Jon will not go to KL.
This brings me to.... Sansa. Middlefinger is a treacherous schemer, but he'll be brought down. I don't know how much influence, if any, that Sansa will have in his demise. Sansa will use her birth, Baelish's help, and her growing skills to be unavoidable in the settlement of peace upon Westeros. Bran and Rickon are presumed dead. Bran is not coming back... and Rickon will die. This means Sansa is the true heir to Winterfell (after Ramsay and Jeyne are exposed or killed). After the deaths of Robert Arryn and Harry Hardyng, Sansa will be the heir to the Eyrie. After the deaths of Edmure, Roslin, their potential offspring, and the Blackfish.... Sansa is the next in line to Riverrun. Remember that against Tywin's wishes but according to the law, Sansa is the Lady of Casterly Rock. At age fifteen or so, she is already (or close to being) the legitimate (no matter who rules in KL) ruler of the North, the Vale, the Riverlands, and the Westerlands. Only the Iron Islands, the Stormlands, the Reach, and Dorne, and the Crownlands would be out of her control. Think back to when she was engaged to Joffrey and almost engaged to Willas.... you could throw the Crownlands and the Reach within her reach as well. She is in position to be a (if not THE) major player in the ultimate resolution of the series. I am convinced that the Starks will continue through the female line in Sansa.
The direwolf pups quickly psychically (spelling?) bonded with the Stark kids. I think Lady did most quickly... becoming un-wolflike... domesticated. Bran is obvisously the most powerful of the Stark children and even though Sansa has not practiced at all, she carries the genes.
If Preston Jacobs' Mendelian Inheritance concepts are valid, then Sansa may carry more genetic possibilites than Dany. Remember that Catelyn's mother was a Whent and descended from the Lothstons (the last two ruling houses in Harrenhal) and carries their genetic markers (the ability to warg bats). Also, with or without marrying Baelish Sansa could make a claim on Harrenhal as well.
In short, I think the story of the Wall is Jon's, the story of the Iron Throne is Sansa's, the story of passion is Robb's, the story of sorrow is Rickon's, the story of hate is Arya's, and the mysteries of the World are Bran's. Fire and Ice? Not sure if it means anything specifically anymore. Not sure if if there really is any super in supernatural in GRRM's world. There are unexplained things, but there are many natural explanations for the supernatural. And I'm convinced anything supernatural will be only low level magic and definitely not anything to do with a capital g God. I now lean to Fire and Ice just being a catch phrase to mean conflict. Hot and cold. Passion and indifference. Even love and hate. All of the Stark kids have these in their stories.