This thread explains the concept of calories well:
Calories are energy. When you digest food, you are breaking down the bonds between each particle, releasing energy that is taken by the body to do work.
From a mathematical standpoint, 1 Calorie = 1 Kilo calorie (scientific energy) = 1000 calories (notice the lowercase) = 4184 joules.
(See also: Wikipedia: Food Energy and ACS: Weighing in on Calories)
Water doesn't have any chemical bonds for your body to break down, so you're correct in that water doesn't have any calories. (USDA: Water has 0 calories.)
Your body does burn calories to bring any cold things you consume up to body temperature. For example, if you eat an ice cube, your body burns energy to melt it:
If one considers that the human body must provide the heat necessary to melt them (around 6 kJ/mol, or 0.079 kcal/g if one substitutes for the molar weight of water) and to bring this (now liquid) water to the average temperature of the body (around 310 K or 37 degrees Celsius), at the average energetic cost of about 0.0755 kJ/mol/K or 0.001 kcal/g/K (constant pressure specific heat of water, source: NIST Chemistry Webbook), and if one supposes the average weight of an ice cube to be 10 grams, the energy supplied by ice cubes amounts to the respectable value of -1.17 (MINUS 1.17) kilocalories per ice cube, and this supposing that they are ingested at their melting temperature (0 Celsius). This means, for example, that the calories contained in the standard Coca-Cola (not Diet Coke!) can (330 mL) are completely eliminated just by adding 148 ice cubes to it.
(...In case the levity wasn't obvious, don't actually eat 148 ice cubes. That's probably a bad idea.)
This is supported by this article, in which Dr. Weiner discusses how eating ice burns calories. A note of caution: Although he concludes that "the ingestion of one liter of ice per day appears to be generally safe" (because Slurpees), he lists the following advisories:
- Don't consume more than one litre of ice per day "to avoid hypothermia or unusual cooling of the body".
- For similar reasons, be extra careful when eating ice during cold weather.
- Don't chew ice, because it could crack your teeth, damage your gums or enamel, or injure your temporomandibular joint.
- For children, the amount of ice ingested should be monitored and related to their body weight and ability to report any problems. Do not put ice into the mouths of children who can't tell you if their brain has frozen.