My only issue with Bran warging into the third dragon is the inherent difficulty with warging into something you don't have a deep connect with.  While dogs are easy, wolves are more difficult unless you have that close relationship to them, which is likely much of the reason why Arya and Jon can do it without really realizing they have the ability to warg.

 

Looking at Varamry Sixskins, who is thought to be one of the most powerful skinchangers, even he notes the struggles with his shadowcat and snow bear.  The shadowcat would violently fight him when he warged into it.  The bear hated him and would rage whenever he would warg into it or ride on its back.  He only attempted warging into a human once (which Bran has done, though to a simpleton), but while unsuccessful, he was on the brink of death when he tried it.

 

I just think warging into a dragon would be a colossal undertaking, and would likely require a lot of time and effort if it is even possible to do with any semblance of control over the dragon.  If anyone could accomplish it, it probably would be Bran.  While I wouldn't be completely shocked if he were to be able to do it, it would be a little surprising to me.  Though, with the three eyed crow telling Bran he "will never walk again, but you will fly," it's probably more likely than I'm giving it credit for.

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