Anyone becoming the Night King or Queen doesn't make sense to me. This story is suppose to be worth telling because it's leading us towards the end. The prophecy is a prophecy for a reason. It's not history. The previous heroes must have failed, because the long nights still came. I think these character are meant to break the cycle and break the wheel if you will. So they'll restore the Earth to how it was before the WWs creation.
Azor Ahai.
I think technically we already know who it is and its staring us in the face. It's Daenerys and Lightbringer are her Dragons. She had to sacrifice her love [Nissa Nissa] to hatch her Dragons from stone. That's why they put her Dragons on the astrolobe in the credits, right underneath the red/bleeding comet. She's depicted as a Mother of Dragons, literally reborn from smoke. It all fits perfectly.
All those signs of "Snow" in Melisandre and Stannis' visions are literal IMO. Jon's real name is not Snow, it's Targaryen. He was brought back with fire magic. Melisandre's fire is light, unlike the ice magic used by the NK. Its the WWs that bring snow and darkness. That's what they're seeing in their visions; Winter snow blanketing the world. It's gonna get freezing cold before it get warm. Jon Snow is represented as a blue flower growing from a wall of ice in Dany's vision, not as snow.
Jon Snow was reborn as well, quite literally. But so was Beric Dondarrion, so i'm not sure that means anything. It wasn't his own miracle, like Daenerys' rebirth. Daenerys used her own instinctive magic. That is what GRRM said, that she used magic. She did something that was never done before. So I think Jon Snow serves to be simply a POV character in the north and as the voice of reason in the plot. His heritage is important because it's important to Daenerys' story arc. She will be faced with a choice.
In the House of the undying she's called "Slayer of Lies" (fAegon in the books) and "Bride of Fire" (because she's marrying another Targaryen? Jon? Or because she's literally married to the element). They tell her she'll light three fires (Funeral Pyre, Vaes Dothrak, ?), ride three mounts (Drogo? to Bed, Hizdar? to Dread, Jon? to Love) and know three treasons (Viserys for gold?, Mirri Maz Duur for blood?, Jorah for love?). I'm not sure about the treasons, they can be interpreted in many ways. I think these three makes sense because they had the biggest impact on her story so far. I'm not sure about the third fire either. Maybe we'll see it this season.
In the House of the undying they also tell her she'll live through "winter, summer, then winter again". It could mean she manages to save the world and witness the changing of seasons.
The tragedy may be that she will not sit the Iron Throne despite her efforts. She might have to burn down as much as she can in order to rid the world of those ice demons. Fire purifies. She will probably resolve to content herself with what's left. A ravaged Westeros and dead friends. It would be bittersweet considering all she'd have lost, but at least the world would be saved.