It's something that I hadn't even stopped to think about. I just took it for granted but it seems that you have to stop assuming. A user wondered, in the Latin American forums, if it was possible to fly on the Island of Quel'Danas and Benzenn gave him an answer:
As I presume you all know the Isle of Quel'Danas, which is at the peak to the north of the Eastern Kimdoms past Silvermoon, is a place that was added during the Burning Crusade boom.
Although it is an area that you can only visit if you have Burning Crusade, it is an area that belongs to Azeroth (the planet), considering this, can we use flying mounts in Quel'Danas?
Greetings.
At the moment, we do not plan to add flying mounts to the Isle of Quel'Danas and Azuremyst Isle.
I'm sure it won't be possible in the Cataclysm release, but we may see it in a later patch because it doesn't really make much sense. I think the problem is that both zones, although they belong to Azeroth, are not part of the same Azeroth (there are loading screens in between to get to them).
And you, did you expect it?