Jon Snow is back from the great beyond, but that doesn't mean every question fans have about him has been answered – far from it. Although the end of "Home" saw Jon gasping back to life, there's still no knowing just what is going on with him and whether he's the same Lord Commander he always was. It seems probable that his experience has changed Jon in some meaningful way, but just how much has death and rebirth altered the hair-tossing bastard we've all come to love? Could he be a different creature entirely? Is Jon Snow a White Walker?
There's precious little to go on just based on episodic information. Viewers only caught a glimpse of resurrected Jon, but there's a lot to go on despite how short the moment lasted. When Jon opened his eyes and took his first breath, those eyes were the same dark brown as always – no sign of the White Walkers' icy blue in sight. In fact, the White Walkers are pretty much icy all over. Even though Jon could stand to get a little bit of a tan, he's far from frozen. Aside from his wounds, he looked just like he always did. That's gotta be a good sign, right?
In the preview for the next episode, "Oathbreaker," there's only a little bit more of Jon. He rises from the table he was laid out on as it cuts to shocked wildlings presumably reacting to Jon being back, while the voiceover (Davos?) says, "They think you're some kind of god." Promos can be misleading, but if we take this at face value and follow the implication that that line refers to Jon, it seems like another check in the Not A White Walker column. The wildlings know all about Walkers; they've dealt with them and fled them and fought them. If Jon was one, they'd certainly know right away.
Jon also hasn't had immediate contact with a White Walker in recent memory. On the show, we've seen White Walkers transform human babies into their own kind with the touch of a finger. No Walker was involved in bringing Jon back; that was all thanks to Melisandre. White Walkers are able to reanimate corpses, but those corpses become "wights," not Walkers. They're basically dutiful zombies, and they've also got the blue-eyed thing happening, so it's probably fair to count Jon out of this one too.
Even though Jon is probably not a White Walker, that doesn't mean everything is A-okay with him. In an interview from 2011, George R. R. Martin said, "I do think that if you’re bringing a character back, that a character has gone through death, that’s a transformative experience... My characters who come back from death are worse for wear. In some ways, they’re not even the same characters anymore. The body may be moving, but some aspect of the spirit is changed or transformed, and they’ve lost something."
That definitely leads me to believe not all will be right with the returned Jon Snow, even if he was able to escape being an ice zombie.