Why would he wish to fight her dragons?
Its not like Bran is pressing for her throne.
Its not like Bran has any motive or agenda just yet bar find 3eyedCrow and survive.
I expect some sort of battle in the snow involving the lord of light and his minions likely assisting by whatever remains of the Dragons, against the white walkers and whoever or whatever they represent.
It'll be interesting to see if Westeros needs to be batter into the ground first to unite the people under one banner to defend against beyond the wall, or if this can take place while the Game of Thrones continues.