Early methods of making ice were discovered in both Egypt and India.
While no single country "made" ice in the sense of inventing modern refrigeration, evidence suggests that ancient Egyptians and Indians discovered methods to cool water, sometimes even freezing it, using evaporation techniques. Around 500 BC, both cultures used rapid evaporation to cool water placed in clay pots on straw beds. The process combined evaporation with lower night temperatures to freeze the water.
Therefore, it's more accurate to say that Egypt and India independently discovered early methods of ice-making rather than attributing it to one specific country.