You can play all your characters on whatever platforms you've registered.

!!! but !!!
If you have Heavensward, you also need a copy of Heavensward for each platform.

If you log out in a Heavensward area on one platform, and then try to log in on a different platform that does not have Heavensward registered, you'll be locked out of that character until you go back to a platform for which you have Heavensward.