[/quote]I didn't think about it at the time, but this gives a bit of a clue why ice is not as conductive as water. In the case of water, pure water doesn't conduct electricity very well because the H2O molecules are very stable. But what water does is provide a medium for ions to free move. So when water is conducting electricity, the H2O is just the medium, but the ions (disolved minerals, etc) move the electricity. When you freeze the water into a crystal structure, the ions are no longer free to move around like they did in the water.[/quote]
(i'm no scientist so this could be wrong)
From what i've learned what happens is that as the ice freezes the ions that allow electricity to flow get "pushed" into the still liquid part of the ice, almost making the frozen part de-ionized. Plus as you say the ice doesn't allow the electrons to move. The colder it gets the less they are able to move and therefore the less it's able to conduct.
Interesting fact...a couple guys smarter than me by far did a test where they added impurities to a block of ice and found it conducted quite well then...almost as good as mercury.