Certain flying mounts (such as proto-drakes or the blue dragonhawk) in Cataclysm Classic can’t be used as ground mounts whilst others (like the gryphons) can. Normally after WotLK patch 3.4.3 you could use all flying mounts as ground mounts in no fly zones.
WotLK Patch 3.4.3 Notes showing Flying mounts could be used as ground mounts: Wrath of the Lich King Classic Patch Notes - Version 3.4.3