Q: AC not blowing cold air in 2003 Toyota Corolla

If the air volume is low coming out of the vents the likely cause is a clogged cabin air filter which should be replaced. This can happen especially if the cabin filter has not replaced in a long time. The air temperature however would be affected either by the AC systems ability to remove heat from the air or possible a blend issue where the cooled air is routed through the heater core. AC gauges hooked up and monitoring the AC system during a performance will be able to narrow down possible causes. Another thing to consider would blocked fins/air passages in the evaporator, either by dirt or icing up of the evaporator. You may want to enlist the help of a mechanic, such as one from YourMechanic, who will have the training, certifications, and equipment to diagnose the exact cause of the air volume/temperature issue with the AC system.