The wife and I started rewatching from the beginning and when Jon Snow first sees a wight at the wall, he throws a lantern at it but burns his hand. Kind of goes against the whole Targarian Blood thing, I guess they could just retcon it or ignore it in other ways...
Good look. I don't see them going down this road. He isn't a dragon. Dany is. It works better for the story if she is unique in that, imo.
His natural +5 at Dragon Handling is enough of a bonus.