Cory Stockton, WoW's lead game designer, gave us a series of informative tweets last night concerning the future of mount type restrictions in the game.
Design decision of the week: We are going to enable all mounts to work in battlegrounds with #Warlords.- Mumper (@mumper) March 14, 2014
Currently you can use ground mounts everywhere that allows for mounting, but flying mounts are, generally, restricted to places that allow for flying. This rule become blurry often, depending on what you consider a ground, flying, or dual mount -- but for example, try to mount up on Ashes of Al'ar in a battleground. You'll find that you can't do it. However in Warlords, presumably with the content patch 6.0, that will become a possibility. The only caveat is that you won't be able to fly on your flying mount in flight restricted areas. This means still, no flying in Battlegrounds.
More of Stockton's tweets from last night after the break.