If you have some knowledge of how the modern air conditioner works, you may know it’s a refrigerant-based system, working in a similar fashion to a refrigerator. To providing cooling, both systems use chemical refrigerant to absorb heat from inside and move the heat to the outside air. This is why the condenser unit outside your house blows out heated air when the AC is working.
What neither system needs to work is ice. It’s easy to believe ice might be involved somehow—after all, the air conditioner is sending out chilled air—but it isn’t the case. Moving heat from one place to another using refrigerant doesn’t use ice. It shouldn’t create it either.