Jon Snow is Dead. Deader than dead thing. He will never be Jon Snow again.
For this I am certain and so it seems is everyone else involved in the TV show.
So Long live Jon Stark ... Jon Targaryen... Azor Ahai... The Prince that was promised.. Jon fire/Dragon
I believe he will come back as another person, or a newly named person with his true identity being revealed. Jon Snow is Dead, but a re-born Jon is going to be with us.
So why I am sure he will come back.
I can't believe the amount of story time in the books and TV to this one character will ultimately end with his death before the resolution of the greater story. Argh you may say, Robb Stark died, catalyn died.
Yes they did, but Lady Stoneheart returned. And Robb Stark may have been given a lot of screen time in the TV show, but in the books his story is more often second hand through other peoples eyes.
Now in the next books and series it seems we may finally get the big reveal that Jon Snow's dad is actually Rhaegar Targaryen. and mother Lyanna Stark. Why create all this back story and reveal his true parentage if he is dead and is staying dead. You wouldn't, It would be the biggest anti climax ever. Yes he is a royal birth but he is dead.
So how does he come back?
I think the night watch burn him, as they would be worried about him coming back as a white walker.
As Daenerys said, flames can't hurt a true dragon. In the flames he will be re-born, just as the dragons were hatched.
I believe he will come back as Jon Targaryen or Jon Fire or Flame (i.e. the bastard son of a Targaryen- I can't find any reference for a name)
But consider, a Stark and Targaryen parentage Jon Snow to Jon Fire. A song of Ice and Fire. His song will be his journey, his life of Ice - his name of Snow and his life on the wall. His re-birth as Jon fire/flame/dragon, his journey of Fire maybe with a dragon.
'The prince that was promised' has a song of ice and fire.
It is clear Rhaegar Targaryen believe it is his destiny to have a son who is the 'The prince that was promised'. Is this why he takes Lynna as she represents the ice?
Most of the signs point to Daenerys as Azor Ahai - born with smoke and salt.
In the books it isn't clear if Azor Ahai and 'The prince that was promised' are the same or two people. Some believe it is the same, but prophecies are open to interpretation. I think they are two different people as the prophecies fit each of them but doesn't work as one person.
So my prediction is Jon Snow is re-born as 'The Prince that was promised' through his song of ice and fire. This is why the King of the White Walkers reacts they way he does.
Only April will tell. It could be that Rhaegar Targaryen. and Lyanna Stark, did fall in love and had a secret marriage. This would make him the true Heir to the Iron Throne.