The question is bit vague. For instance, if some water has already condensed in the atmosphere as fog, collecting it is much easier than condensing dry vapour from the air with human means.
Also, I'd rather collect liquid water from the air, and freeze it in a separate location. This lets you cool the air less, and can produce ice with the best shape for you needs.
Up to now, humans freeze water by the contact with a cold solid. As the ice cap grows, it insulates the surface from the cold solid, so further growth is slow, like <10cm overnight. I propose therehttp://www.chemicalforums.com/index.php?topic=46384.msg257744#msg257744
to freeze new water by a cold gas instead, which isn't limited by the ice thickness. Though, said gas shouldn't be the ambient air, because cooling new air all the time would be a waste.
But if power isn't a limit, just cool the air by expanding it a lot, and filter out the snow. Quick, and huge waste.