Yes, it does. Conductivity is directly related to the impurities in the ice. Electrical properties of ice have been studied to a great degree over the last 20 years, especially in the Antarctic.
Coldfuse is right about the impurities, but the question asked about ice and in the case of pure distilled water which has been frozen into ice the dielectric strength is very high, making it an excellent insulator. Hi coldfuse, I used to be frankvan at AP.