It takes 1 calorie to increase 1 ml of water 1.0 degrees celcius. Freezing temp in Celcius is 0, and body Temp is 37. 1000 calories make up 1KCal which is actually what food calories are.
So lets say you drink 4 liters (about a gallon) of ice cold water each day. Thats 4000 ml. Lets assume the water is near freezing (0 degrees celcius).
calories=4000ml*(37- 0 degrees C)*1.0 cal/(ml*degree)=148,000 calories.
But don't get too excited, cause 1000 calories is actually only I food calorie (KCal)
So dringing 1 gallon of freezing cold water will burn about 148 Calories a day. Not that much, but its something.