Many would say that its Jon Snow because:

1. He is child of Rhaegar Targaryen(Fire) and Lyanna Stark(Ice)
2. He is bought back to life by R'hllor the Lord of Light and thus is marked by him while at the same time he wields Longclaw one of the Swords of Winter( Ice, Heartsbane etc.)
3. Rhaegar was a great believer is the Prophecy and thus he fathered a third child(a dragon must have three heads) with Lyanna to set it in motion, sacrificing himself at the Trident so Jon Snow remains unheard and safe from Robert.

However there is another player in the books namely Aegon Targaryen II who did not die during the sack of Kings Landing. It is very likely that he is the Prince that was Promised because he holds allegiance to both Fire and Ice as well.

The real question is regarding R'hllor. Is Jon Snow's return(not in the books) indicating him as more deserving of the title of Azor Azhai? Or does Aegon Targaryen's true fireborn blood make him the true dragon after Daenerys?

It all boils down to books vs show in the end.