Well, I don’t think it’s really an equivalent to the Night’s King. I think it’s an equivalent to Sauron:
“Finally he looked north. He saw the Wall shining like blue crystal, and his bastard brother Jon sleeping alone in a cold bed, his skin growing pale and hard as the memory of all warmth fled from him. And he looked past the Wall, past endless forests cloaked in snow, past the frozen shore and the great blue-white rivers of ice and the dead plains where nothing grew or lived. North and north and north he looked, to the curtain of light at the end of the world, and then beyond that curtain. He looked deep into the heart of winter, and then he cried out, afraid, and the heat of his tears burned on his cheeks.
Now you know, the crow whispered as it sat on his shoulder. Now you know why you must live.”
That’s not a dude throwing javelins, that’s a dark god who dwelleth beyond the northern lights, staring back at you from the abyss.