It’s likely Bran can warg into a living dragon. Whether he can warg into the Night King’s undead dragon Viserion is a different beast entirely. It seems unlikely even someone with Bran’s incredible abilities could control a creature resurrected by a magical ice demon. However, in his quest to destroy his most dangerous enemy, the Night King might have unknowingly given Bran that awesome power when he touched him, just like how Voldemort inadvertently made a direct connection between himself and Harry Potter.
White Walkers raise the dead without touching them – except, quite notably, when the Night King brought back Viserion by placing a hand on him. The bond between Walker and wight is very strong; when a White Walker is killed, all the dead soldiers they resurrected die too. The Night King and the still-very-much-alive Bran also have a mystical bond.
In season seven, Bran warged into a raven to do reconnaissance beyond the Wall, and he spotted the army of the dead near Eastwatch. As he soared over the tens of thousands of wight soldiers, he passed the White Walkers, and as he did the Night King stared right at him. He knew Bran was there watching him, and Bran instantly left the raven and opened his eyes back at Winterfell’s weirwood tree.
Maybe the Night King can sense the presence of any warg nearby, but we know what it took for him to find Bran and the Three-Eyed Raven originally. In season six’s “The Door,” an impatient Bran went into a vision alone. There he found the army of the dead. Bran walked through the wights who didn’t move, unaware he was there. But when Bran walked up to the White Walkers on horseback, the Night King looked right at him. Despite not physically being there, the Night King could clearly see Bran then too.
The rest of the dead then turned to look at Bran as well, and when he turned back the Night King was standing next to him and he grabbed Bran’s arm. Immediately Bran woke up back in the cave of the Three-Eyed Raven, where he said the Night King had seen him. The Three-Eyed Raven told Bran the White Walkers now knew where they were and would come for them soon. When the dead arrived, the magical spells keeping the Children’s cave safe were gone, as White Walkers and the dead went in without exploding like they had before. If you need a reminder, everyone except Bran and Meera died because someone held the door.
The Night King’s powers let him do the seemingly impossible. Bran was in a vision, but he saw him. Bran wasn’t physically there, but the Night King touched him. That let him both know where the Three-Eyed Raven’s cave was, and it broke the magic that had kept it safe from the dead. That’s a connection beyond anything else we’ve seen in Game of Thrones, and to find a parallel we need to head to Hogwarts.
On two separate occasions, Voldemort, another soulless killer set on world domination, inadvertently bonded himself and Harry Potter in ways that ultimately helped destroy the Dark Lord. The first was when Voldemort’s attempted murder of Harry. Voldemort’s arrogance blinded him to how Lily Potter’s sacrifice cast an old type of protective magic, and he accidentally turned Harry into a secret Horcrux, connecting their minds and souls. That’s how Harry was able to see and experience important events and insights through Voldemort’s mind, and how he gained some of Voldemort’s powers in him (like how Harry could speak Parseltongue).
Voldemort made arguably an even greater mistake when he used Harry’s blood to regain a body. That tethered the two yet again, and when Voldemort finally did “kill” Harry, Lily’s magic lived on in Voldemort, which kept Harry alive.
“I don’t know, he was close but-” Bran answered.
“He touched you,” said the Three-Eyed Raven with conviction, “He knows you’re here. He’ll come for you.” He then told Bran the magic of the cave wouldn’t work anymore, because the Night King’s “mark” was on him. The blue spot on Bran’s arm proved the (dark) mark was not metaphorical. But how did the Three-Eyed Raven know the Night King had touched him? Is it because he could see through time and knew it would happen? If so, why did the Three-Eyed Raven let Bran go into that vision alone in the first place?
Because he wanted the Night King to touch Bran.
Physical contact was the only way to create an intimate connection between the two, just like Voldemort had with Harry. The Three-Eyed Raven couldn’t leave the cave himself, his ancient body was only kept alive thanks to the deep roots of the weirwood tree, but Bran is young and can still return to the land of the living to help fight. This seemingly terrible mistake by Bran was a brilliant, secret plan by the wise Three-Eyed Raven who was four moves ahead of everyone in a game they didn’t know they were playing. He pulled a Dumbledore.
Bran being bonded with the Night King would answer the questions raised by the theory that says they are the same person. Harry wasn’t Voldemort, but they shared parts of their mind and soul. And if Bran is connected to the Night King, he’s also connected to the Night King’s dead dragon, the only dead creature we ever saw the Night King physically touch to resurrect.
We’ll find out if Bran can warg into a dead dragon and neutralize the dead’s greatest weapon, but thanks to the Night King it certainly looks like he has the right touch to do it.