The best description of a morphed creature(I'd say face down, but then there's illusionary mask...) is that it's under an effect, that to end the effect, you pay the morph cost to turn it face up.
But it's not an activated ability...
Hmmm, that means that if there's a city of solitude in play -
City of Solitude
Color= Green Type= Enchantment Cost= 2G VI(R)
Text (VI+errata): Players can play spells and abilities only during their turn. (Triggered abilities are unaffected.) [Oracle 1999/07/01]
The morph cost can be paid and the creature turned face up during any turn... hmmm...