A set of Continentials on the back does nothing to aid in your turning and braking on ice and with more drag on the back only, it may give you more problems.
Spiitz is right about the ABS system also, if it doesn't work on ice, then it isn't working!
You need a good set of snow tires like the Blissaks and then in the summer put on the Pilots. Putting on Continentals will give you so so winter tires and the Pilots are great summer tires. The Continentals like I have, are OK as I can use them for both but if you are going to keep the Pilots then don't get the Continentals as there are better "winter only" tires.