Would no antifreeze stop car from blowing heat in winter?

No antifreeze (coolant) in a car's cooling system would almost certainly prevent it from blowing hot air in the winter. The coolant is crucial for transferring heat from the engine to the heater core, which then warms the air blown into the cabin. Without coolant, there's nothing to carry that heat. Furthermore, running the engine without coolant will cause it to overheat very quickly and likely cause significant engine damage.