I rewatched S7E6, “Beyond the Wall”, again and noticed a few things I had not noticed the first time.
For one thing, it almost seems like the Night King knows when Bran is watching him through Greensight. Is it just me? When Bran had warged into the ravens to fly over the Army of the Dead, the Night King looked up and the ravens scattered immediately, as if the connection to Bran had been suddenly interrupted or broken. And since Bran immediately goes out of his warg/Greensight trance also, I am assuming that it is broken.
The Night King was created by the Children of the Forest. Did they pass on Greensight to him when they created him?