Yeah, yeah, we know Jon Snow's a Targaryen. That's not even a theory now, it's been established as fact on Game of Thrones. But the show isn't completely done with the mysteries and sneakiness—particularly where it applies to King in the North/dead man walking Jon Snow, because the penultimate episode of Season 7 dropped a major (yet subtle) hint about his future.
It's fair to say that GOT is deliberately vague when it comes to magic—partly because too much exposition is boring, partly so it doesn't paint itself into a narrative corner further down the line. We don't know the limits of Arya's magic, we don't know how Bran's warging and greensight work, we don't know how White Walkers animate the dead—and for the most part it doesn't matter. We trust that either we don't need to know, or that we'll find out later.
Jon Snow, though, is dead. He died. He was brought back to life by Melisandre—even she doesn't really know how—and somehow he continues to walk about, eat sandwiches and have sex with his aunt like any other perfectly normal person.
Gregor Clegane also died (or came very close) and was brought back to silent, lumbering life by Qyburn using his alchemist's science. Beric Dondarrion has been brought back six times the same way as Jon—though as the "six times" thing suggests, he's very capable of dying again, for good. But is Jon? It would be reasonable to assume that yes, he's still mortal—like Beric—but that might not actually be the case.
Look again at the scene in episode six where Jon is dragged down into the freezing waters of the lake. He misses the last flight out of town, everyone thinks he's done for, and Daenerys and the remainder of the Magnificent Seven all flee the scene on dragon.
When we cut back, seemingly moments later, Jon pops up out of the lake, grabs Longclaw and is about to make his last, solitary stand when Uncle Benjen rides to the rescue. But is that what really happened?
When Jon emerges from the lake, the wights have cleared the field. How long does it take an army to depart a frozen lake? An hour? Maybe a well-disciplined army could do it in half that. Maybe an army of dead people controlled by a single intelligence could do it in even less. Let's be super-generous and say that even allowing for slippery ground conditions, stumbling animated corpses, and the lopped-off zombie parts getting underfoot, it takes an army of wights just 10 minutes to clear the lake.
That means Jon was underwater for twice as long as any normal human being. Yes, free divers with years of training and preparatory hyperventilation can go for 22 minutes in nice, warm water—while wearing Speedos. Jon was in a frozen lake wearing 40 pounds of leather, iron, and fur.
Here's our point: if the showrunners intended to hint at what we're inferring from the scene, then Jon is either immortal, or he has a superpower. If he's immortal, that could solve the "break the wheel" problem of the show's resolution—namely, how do the good guys stop the endless cycle of tyrants running Westeros? By having an immortal benign dictator—a good king forever—even if Jon would prefer otherwise.
Let's say he's not immortal, though—maybe he's immune to ice in the way that his aunt is immune to fire. It would be a nice symmetry and a useful skill in the coming battle with the Night King and his ENORMOUS ICE-BREATHING DRAGON. Well, his blue-fire breathing ice dragon. It's not totally clear what Viserion is now.
Anyway: Jon Snow. The Snow Man. It's there in the name, FFS.