The Great Intelligence made a big noise about the final atrocities that the Doctor committed before his death. Deaths of Billions. In my mind there is no way that the John Hurt Doctor is from the past.
But then the doctor wouldn't know who he is or what he's done, and apparently the Doctor has been carrying this burden for a very long time, but if its a future incarnation, he wouldn't know yet, so that doesn't make sense that Hurt is a future incarnation.
I rewatched the episode last evening. I was initially dismissive of the idea that John Hurt could be a future Doctor; the dialogue at the end clearly indicates that the eleventh Doctor knows what Hurt did, which indicates the past.
While I'm still sure of that (for other reasons, which I'll address), the episode does offer another possibility.
Think about what the Doctor did immediately prior to saving Clara from the fog and meeting John Hurt.
He jumped into his own timestream. And we know from dialogue earlier in the episode that the Doctor's timestream extends to some point in his own personal future. While Clara didn't see the future Doctors (per dialogue), there's nothing that indicates the Doctor also didn't. The Doctor
could have seen his own future, his incarnations yet to come, and what those incarnations did. Therefore, he could have known what horrible things the Hurt Doctor did, even though, from his perspective, it hadn't yet been done, and thus he passed judgment on his future Hurt incarnation and his actions, dubbing him unfit of the name "Doctor."
All of that said, the dialogue between Clara and the Doctor contradicts much of that speculation, as they talk about Hurt in terms that indicate that he was in the past times where Clara went. Plus, Hurt is a secret the Doctor keeps; that doesn't make sense if the Doctor had just discovered that his future self is a horrible creature. These all point to Hurt as a past Doctor.