Ice has no calories, sure, but it does require some input of energy to keep your body warm (or at least your mouth) if you're intent on eating ice. Where does that heat come from? Well, from the burning of calories, of course.
FWIW, I noted weight loss in winters, when I was growing up. Not usually significant, but usually there. I've heard that if you turn down the temp 2-5F in winter, you can lose a couple of pounds from the extra heat required to keep warm. I usually eat more when I'm cold. It all fits together for me ...
Now the trick is to say "You too can lose weight on Dan's new 'Freeze-yer-donkey-off' diet" in 250 pages with nifty little pictures and classy cover art. I swear if I do it and sell a million copies I'll donate heavily to Pelican.
Dan