Bran Stark may be the Three-Eyed Raven, but his contribution in the Battle of Winterfell definitely proved to be somewhat underwhelming. Many thought he would've played a much bigger role in taking the Night King down (like warging into Viserion or killing the Night King himself). But what if that isn't the end of his story? Perhaps his big warging moment is still to come in the Battle of King's Landing. But can Bran warg into a dragon on Game of Thrones? You would've thought he'd do it during the Winterfell battle to help even the odds a little better. However, just because he hasn't done it so far doesn't mean that he can't ever do it.
Since the very beginning of the series, it felt like Bran was destined for something special. Not only can he warg into the minds of animals, but he's also a Greenseer, allowing him to see both the past and the future. One could argue that if Bran is able to warg into animals, then a dragon should be no problem, though nothing on Game of Thrones is ever as simple as all that. Warging into a crow or a direwolf is one thing, but taking a massive magical being like a dragon is a whole other ballgame. That doesn't mean it's impossible, but it could prove to be much more tricky.
Sadly, none of us possess Bran's knowledge of the future, so we can't say with absolute certainty if he'll ever even get the opportunity to try it. But if he does, here are a few clues that suggest he'd be successful.
He's Defied Warging Challenges In The Past
Wargs are known for controlling the minds of animals, but Bran took his power to a whole new level when he was able to delve into the mind of an actual human: Hodor. That right there proves that Bran's powers could potentially achieve something that no one else's could.
The Three-Eyed Raven's Message
During an interaction with his Three-Eyed Raven predecessor, Bran hoped the man's powers would help him be able to one day walk again. The Three-Eyed Raven responded by saying: "You will never walk again, but you will fly." Sure, one could interpret that in a variety of ways (he could've been referring to a crow or hinting at how Bran would be able to fly through time), but maybe, just maybe, it was foreshadowing Bran ultimately warging into one of Dany's dragons. That would give him the ability to fly.
The Night King Did It
The Night King and Bran have always shared an interesting and complicated connection. (Heck, many believed Bran actually was the Night King.) So is it possible that they could share similar powers as well? The Night King was able to resurrect Viserion and control him as an ice dragon. Bran may have the ability to do the exact same thing with dragons that are still alive. After all, if Bran and the Night King are opposite ends of the same coin, then their powers should mirror each other. The Night King controlled the dead, so Bran may be able to control the living.
This is all just speculation for now, but with only two more episodes to go, time is of the essence. So if Bran is planning to warg into a dragon at some point in the future, he better do it fast.