Oh, and Mormont never gets greyscale in the books like he does in the show. The showrunners were basically combining his storyline with part of another character's, who hasn't appeared in the show: Jon Connington.
Jon Connington is supposed to be escorting young Aegon Targaryen, Rhaegar's son, who isn't dead, to see Daenerys and then over to Westeros during "A Dance with Dragons." He's been watching over Aegon since he fled King's Landing. But he gets greyscale while pulling Tyrion out of the water (just like Jorah did in season five). Jon hasn't appeared in the show and this may be a sign he won't.