While we know he definitely has access to the past and such, he has had glimpses of the future. In one of his visions they show an image of a dragon's shadow flying over King's Landing. They then had almost the exact same image, but with Drogon and Dany in this past episode. So I think they have shown he can have glimpses of the future. Like doesn't have the power of 'Greensight' like what Jojen Reed had? Jojen had visions of the future and that is why he found Bran. He even saw his own death before it happened. Doesn't Bran have that same, if not more, power?? That is how I looked at it at least.