There is some evidence that large, loose, icy comets are constantly bombarding Earth from space in roughly the correct rate to account for most all water on Earth. The supposition is that they are not near-Earth objects, but rather from far away and thus bombarding at least Mars and the Moon, if not the whole solar system. A rather tenuous extension of this is that these icy-comets may be quite common within galactic space (at least near us) and most nearby stars (and thus any planets near them) would get water. Of course keeping water is another story.
I looked into it and the press release from NASA doesn't specify water-snow. Technically, snow should be water - but then again ice should be solid water and they specify water-ice (in the same release) to distinguish it from carbon dioxide-ice. NASA has a history of this kind of thing.