What’s Next for Jon Snow on Game of Thrones?

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"Even if the resurrected wights have no bearing here, Jon's return may not entirely be a good thing. As George R.R. Martin has said before, "My characters who come back from death are worse for wear. In some ways, they're not even the same characters before. The body may be moving, but some aspect of the spirit is changed or transformed, and they've lost something." In other words, he could come back wrong. This is how the showrunners and Kit Harington can get away with saying that Jon Snow wasn't coming back this season — whoever this is now, he may not be the Jon Snow you knew and loved.
His personality could be altered. We'll let Beric Dondarrion, who has the most experience in these matters, explain what being brought back to life has done to his humanity: "Every time I come back, I'm a bit less," he says. "Pieces of you get chipped away." Beric, at least, had some empathy left, but that could be because Thoros of Myr would perform the ritual immediately after his death. Jon's body had some time to get cold, and that could affect his ability to feel. (A separate deceased character from the books, Lady Stoneheart, was left cold for three days before her resurrection, and she has, well, a stone heart as a result.)
more in Jennifer Vineyard's analysis
What’s Next for Jon Snow on Game of Thrones? -- Vulture