If you ate one kilogram of ice, you would burn 80 calories in converting it to water, and another 37 calories
to raise the water to body temperature, for a total of 117 calories. So, for every five-pound bag of ice you managed to chow down, you'd save yourself roughly 265 calories. Have fun chewing on that much ice
Even then, there's another nagging problem. The human body deliberately loses about 75 calories per hour to the surrounding environment, in order to avoid overheating. If you were to eat ice and throw that out of balance, the body would compensate by not sweating as much, in order to avoid losing too much body heat. If you do manage to overcome this, your body temperature will begin to drop, but you still won't be burning energy until you begin to shiver, which is the body's last-ditch effort to keep body temperature normal.
You might try a different strategy than shivering away calories: you could maintain the heat balance by doing more physical work.
But you were trying to avoid exercise, weren't you?