This is my own theory, as a book fan, on why Jon Snow may still be alive.
"'Ghost,' he whispered...He never felt the fourth knife. Only the cold..."
This part leaves me to believe that Jon warged into Ghost before he died. Therefore, Jon is alive, as Ghost.
In the books, Jon is repeatedly portrayed as a warg, just like Bran Stark, but a little less trained in the art of warging as Bran was. Nevertheless, Jon is a skin-changer: he can transfer to Ghost's skin at will.
The prologue of "A Dance with Dragons" tells the account of Varamyr Sixskins warging into a wolf moments before his death. What was said in the prologue was thus:
"True death came suddenly; he felt the shock of cold...Then he found himself rushing over moonlit snows with his packmates close behind him."
This prologue was not for naught; it means something. GRR Martin would not have included this part had it not have some profound context to a major plot in the story.
For those questioning where Ghost was during Jon's death, here's what happened in the books: Jon commanded Ghost to stay behind, since he was to hold audience amongst the Crows and the wildlings, with one of the wildlings Borroq having a "pet" boar. Boars and direwolves are fierce foes by nature, and both Borroq and Jon do not wish for their pets to kill each other. Thus, Ghost must be left behind, away from Jon, so as not to provoke the wildling boar.
Here's my theory: Ghost was out hunting, or somewhere inside Castle Black, where the snow and cold were fierce in their coming as winter commenced. That is what is meant by Jon only feeling the cold as he was "dying": his soul was fleeing to Ghost's skin, and therefore, he lives.