The radiator will get it closer to ambient temperatures, just like snokamel said, and when the said radiator is inside of a freezer, it will get the water temperature colder than just using a reservoir inside the freezer.
Besides that, if there is an area of the reservoir that does not get a lot of flow, it could start freezing the water, and this would be bad because it would make the water thicker, thus taxing your pump and slowing it down. If you used a radiator, there are no spots in which there is no water movement and so the water won't be in long enough to freeze yet it gets real cold, heh.
Antifreeze will work better in the mixture than alcohol I belive.