I've been mulling over this for a while, and finally decided to post (usually I lurk).
Danaerys likes to talk about breaking the wheel. But I was most interested in the tidbits about the Targaryen line being nothing without the might of their dragons. They came to power only because of their dragons. And then lost their power as their dragon became no bigger than cats. She said something like, "We diminished."
So if the only way to stop the WW and NK is the end all magic (including the dragons), then the GoT ending would be a world without magic. Which is bitter for many there and yet brings hope of a real life without the Wall and worries about a future Winter coming that could destroy them all.
How can a Targaryen rule in such a world?
How do Starks live in such a world?
The people, including the remaining Targs and Starks, all start over. Maybe that's the true breaking of the wheel.
In thinking about the GRRM's fondness for the bittersweet ending of LotR: The bittersweetness reflected the huge change in the world: the end of the Third Age. The Elves (magic) departed / diminished, leaving Middle Earth to the realm of Men. A similar ending for Westeros would be the loss of mystery and wonder, and the move toward an average-man's life. That is, no more magic: dragons, CotF, WW, NK, the Wall, and maybe even the Lord of Light / Red Priestesses. Westeros won't be the same Seven Kingdoms, and the Iron Throne would no longer matter (probably won't even exist). Westeros that was becomes history, similar to Valyria. (What goes around comes around.)
So, Jon and Dany might survive but they won't be ruling Westeros because it pretty much no longer exists as a kingdom or a kingdom of little kingdoms. Most of the little kingdoms are wiped out.
Jon & Dany's ending
If you're a major character, you often get what you need not what you state you want in the beginning of the story. Because you're supposed to grow over the course of the story. And usually realize that your early wishes were unfounded immature beliefs.
Once she learns to take charge of her destiny, Dany wants to live with her husband and child. She thought that was all lost when Drogo and her son died. When that dream ended, she spent a lot of time and effort trying to get her birthright. It's a lot of work (and several TV seasons) to get even close to the Red Keep but she won't complete that quest because of the WW & NK. So she'll end up with what she really needs: husband and child in the form of Jon and boatsex-baby, possibly more kids. With a changed world, she won't need to be Queen of the Andals, [insert a million titles a la Aragorn here].
From the start, Jon never expected to be a leader or important, but he became both and wasn't exactly happy. [Dany: 'We all like to do what we're good at.' Jon: 'I don't."] He wanted to know about his parentage -- well, he'll learn that but will it make him happy? Throughout the story, he is moved closer and closer to the center of the primary conflict, eventually becoming a major player for the climax. And yet, Jon is most like the Samwise Gamgee of GoT -- a nobody thrust into huge events who does what needs to be done for the good of everyone.* And like Sam, he most likely will return to a simple life, with the sad knowledge of how the world has changed and how much he or those he fought for and protected have lost. He'll always feel the pain of knowing that he couldn't save them from those losses. But be happy with what he has: knowledge of who he is and having loved ones around him.
*Sam takes on the burden of the Ring when he believes Frodo is dead. He contemplates gathering an army, raising his flaming sword, and challenging Sauron, then realizes that he couldn't win that fight. He 'knew he was not large enough to bear such a burden... The one small garden of a free-gardener was all his need and due, not a swollen garden to a realm; his own hands to use, not the hands of others to command." Instead, he determines to fulfill the quest and enters the scariest place in Middle Earth. A few chapters later, he willingly returns the Ring to Frodo. Then he literally carries Frodo up Mt. Doom. He gets that garden in the end, and honors that are due to him. But he's sad that it came at such a huge cost to his friends and his world.