Please, no more need for recycling the same old theories about why he is alive. That ground has been thoroughly covered. That horse is as dead as Jon Snow.
Of course there actually are some decent arguments for why Jon Snow might somehow be resurrected. That possibility seemed quite plausible in the books, with Melisandre's presence at the Wall providing for a means of bringing Snow back from the dead -- and when Melisandre made her retreat back to the Wall as Stannis's army fell it seemed fair to ask why else she would be there but to save Jon Snow. The books also resurrect... book spoiler warnings Catelyn Stark. The books introduce a character, Coldhands, who seems to be a different form of living dead from the other creatures found north of the Wall.
In both the show and books Gregor Clegane, The Mountain, is brought back as some sort of zombie. Beric Dondarrion is resurrected several times before (in the books) passing his power onto Catelyn Stark. There would have also been the possibility of glamouring, as we know that Melisandre can make one character appear to be another. The book also emphasizes wargs, with some theorizing that Jon Snow could have warged into his direwolf before his body died (never mind that there's no obvious way back to human form, and that we've been told that remaining too long in an animal host will cause you to lose your human character).
Also, it seems like an incredible waste of a very interesting character to kill Jon Snow at this point in the story. The relationship you form with a television character is different from that you form with a character on the printed page, and the loss of Snow seems all the more stark (no pun intended) in the series. Why spend all of that time and energy building him into an interesting character only to kill him off, with nobody else of similar charisma to fill his shoes? Why drop conspicuous hints about his "real" parentage if he plays no role in the end game? From a literary standpoint, why kill off the principal point of view characters who could play a central role in the conclusion, while keeping alive others who can't possibly be on the winning team? Will people, readers or viewers, care about events at the Wall without Jon Snow?
At the same time there's one consistency to Martin's writing: If you're a noble, virtuous character who puts the well-being of others ahead of your own, you end up dead. Do you really think that Snow's body will be hidden and frozen for a year, so that he can be resurrected in Season 7? (Jon Snow on Ice.... Is this a Disney production?) From the standpoint of good storytelling, as questionable as it may be to kill Jon Snow at this point in the narrative, a secret, frozen Jonsicle would seem to be worse.
I suspect that the future story anticipates that readers won't care about the Wall post-Jon Snow, and thus won't be surprised or offended when the army of the dead defeats the remaining members of the Night's Watch (and any Wildlings who might have inexplicably continued to support their efforts in the wake of Snow's death), creating the context for a major conflict between the advancing White Walkers and the dragons of Danaerys. (That story line would seem a bit... predictable. We'll see.) Also, particularly if Jon Snow has the royal blood that many plausibly believes used to run through his veins, we can expect Melisandre to have some interesting visions in the flames of his funeral pyre.
The primary evidence for Jon Snow's death comes from the show, (and if it needs to be said) not the as-of-yet unfinished, unavailable sixth book. The show did not renew Jon Snow's contract for Season 6. It's one thing to give a character like Bran a year off, without much concern for whether the part will have to be recast in a future season -- children and adolescents change a lot, and few would be surprised to discover that Bran looks different after a year of communing with ancient trees -- he'll look different even if they keep the same actor.
While daytime soap operas of old used to switch out adult characters without much concern for appearance, and Game of Thrones has done the same with at least one small part (Gregor Clegane) and with a smaller role before it became larger (Tommen Baratheon) I don't think that audiences will accept a different actor as Jon Snow. He could come back among the undead, perhaps as a hooded Coldhands-type character, but he would both be dead and be a very different character -- what would be the point? If the show wanted to be sure that Kit Harington would be available to play Jon Snow in Season 7 or beyond, given the difficult production schedule, it is highly unlikely that they would risk his taking other jobs that would prevent his participation.
The show understandably shares Martin's affinity for killing off characters -- but sometimes the reasons for a death seem different, such as to simplify story lines and perhaps to control the show's budget. The death of Ser Barristan Selmy (a character whose story line died a slow on-screen death even before the showrunners made it final), the death of Mance Rayder with no glamouring, moving up the death of Shireen Baratheon and the defeat of Stannis Baratheon, not bringing back Catelyn Stark, killing Myrcella Baratheon (who at this point in the books was only missing an ear)....
The showrunners could easily have carried Jon Snow's character forward into season six, perhaps drawing on the chapters dealing with his management of the Wildlings or delaying the death of Stannis Baratheon while having Jon Snow announce the rescue mission that precipitated his death on the printed page. But they instead chose to bump Snow off during the last episode of the season, saving themselves a big chunk of change to apply to hiring other actors, building sets and producing special effects.
If in light of all of that you still think Snow is coming back, what do you think the dialogue would be upon his return in season seven? "Hey, folks, I'm back. Did I miss anything? Ooooh... are those dragons?"
So stop watching the length of Kit Harington's hair -- it's going to get longer and shorter over the coming year because (assuming an occasional haircut) that's what hair generally does. Stop arguing that if you turn your head sideways and squint, you can see proof of Snow's survival because his eyes almost imperceptibly change color during his death scene. "We shall never see his like again, and now his watch is ended."
