Silly -- the moon was formed from the recently discovered "cheesy asteroids."
The moon wouldn't have been able to retain the water, however.
That's true. The moon is much smaller, though, and doesn't have enough gravity to retain an atmosphere. So if we land an icy comet on the moon for the water, we would have to throw a tarp over it right away or it would all eventually just boil off.
They might, but the lack of atmospheric pressure and gravitational atraction would cause sudden evaporation into space like the primordial atmosphere the moon once owned .