Martin has very strongly hinted that Jon isn't dead.
The obvious possibility is that he warged into Ghost before physically dying (which makes sense since the ADWD prologue shows Varamyr Sixskins doing exactly that.)
I hope that's not the case.
Burning shafts hissed upward, trailing tongues of fire. Scarecrow brothers tumbled down, black cloaks ablaze. "Snow," an eagle cried, as foemen scuttled up the ice like spiders. Jon was armored in black ice, but his blade burned red in his fist. As the dead men reached the top of the Wall he sent them down to die again. He slew a greybeard and a beardless boy, a giant, a gaunt man with filed teeth, a girl with thick red hair. Too late he recognized Ygritte. She was gone as quick as she’d appeared.
"Armored in black ice" reminds me of Coldhands. If Coldhands really is Benjen Stark, maybe Starks can't become Wites if they die beyond the Wall. Maybe they become the opposite of White Walkers/Others. They turn black and keep their consciousness. Maybe it has something to do with the spells woven into the Wall when Brandon the Builder constructed the Wall. He was a Stark after all.