Ice itself is a negative calorie.
However when you eat ice the ice causes your body to burn off some calories because your body needs energy to melt the ice.
Eating ice or drinking a glass of ice water rather than a glass of water at room temperature only burns about eight calories.
Your basal metabolic rate, which keeps your organs functioning, burns about 70% of your calories.
Similar to chewing, drinking cold water does expend some calories.
However, such small effects will not substantially increase the calories your body burns.
Though some calories are used to chew, digest and process foods, it's probably a fraction of the calories the food provides — even for negative-calorie foods.