Spoiler alert. I'm just guessing, but Matt Yglesias has gone public so why can't I ?
I am confident that he will turn out not to be dead if Martin ever finishes the next volume (and in the outline which he has written down in case he doesn't live that long). The reason is that, like most hard core fans, I have long been very confident that he is the son of Rhaegar Targaryan and Lyanna Stark.
I have a further guess. "A Dance with Dragons" ends with the stabbing of Jon Snow. He loses conciousness (which is not the same as dying as I notice at least once a night). Just before, there was a fairly extensive scene featuring a giant prisoner (whom Snow was trying to help). It seems fairly clear to me that this giant would break his chains and save Snow. There is a reason to have him near at hand. Snow also has strangely good relations with Melisandre of Asshai who is perfectly capable of just about anything (including breaking chains which hold a giant). Also Ghost and Mance Rayder who, in the books, is not a ghost.
OK now Snow's actual parents. I think this has been clear since book 1 (the one actually entitled "Game of Thrones").
Here Eddard Stark repeatedly remembers his sister forcing him to promise something (some things actually as there is a single reference to plural "promises"). Her death is not explained (and childbirth is dangerous in Westeros).
As Yglesias notes, Rhaegar's alleged kidnapping of Lyanna Stark is totally out of character. He is presented as a very moral person very much admired by everyone who knew him.
One problem with Yglesias's post is he considers the possibility that Rhaegar and Lyanna might marry. Rhaegar was already married to a Martel at the time.
On the other hand I missed the capital S in "all I see is Snow". This might explain Melisandre's interactions with Jon Snow (among other things revealing that Rayder is still alive and trying to convince him to stop fighting his nature).
Finally Belarion the dread -- is among other things the nickname Rhaenys Targaryen gave to her black kitten. An old black cat which hates Lannister's (and has only one ear) has appeared more than once (chased by Arya Stark then much later scaring Tommen Lannister). I assume they are the same cat. I also assume that Arya Stark will see through the eyes of Belarion).
But who is the third head of the dragon ? The only candidate of whom I've read is Tyrion Lannister on the assumption that he is Aerys's bastard. I thought of Brandon Stark who is destined to fly (but that might be as a crow).