Yes. Here are a few reasons:
1. Most human pathogens (viruses and bacteria) multiply best at an ideal temperature which is just below normal body temperature. Ice will lower the temperature in your throat.
2. A decrease in temperature causes local blood vessels to constrict, thereby decreasing the blood flow. White blood cells cannot easily reach there to fight off the infection.
air and water / ice has a desiccating (drying) effect on the delicate mucosa (lining) of your throat and respiratory passages. This disturbs the normal mucus blanket and increases irritation and may worsen your cough