Sure -- the only diff between calories and Calories is that Calories are really Kilo-calories.
Either way, sucking on ice will consume calories, but very slowly. Let's say your average daily diet is 2500C (or Kc, whatever), and you need to burn an extra 500-1000C (or Kc) in order to maintain a good steady weight loss. Assuming you do no workout, do not alter your diet in any other way, etc., you'd need to consume 625-1250g of ice, which is (wait for it) about a liter of water, give or take.
So if you daily took down about a quart of ice, you'd dump like 800C, which would be nice. It may not seem like much, but I'll bet that's a bunch after you've actually done the deed. Alternately (and people who live in cold climates can attest to this), you can spend time outside in the cold, inadequately bundled. Your body will compensate by generating more heat ... or coming down with hypothermia, if you push this weight loss method too aggressively.
Anybody want to do the experiment? How painful is it to take down a quart of ice?
Dan