The answer to 'evaporator coil blowing cold air' is that the evaporator coil is likely freezing up, causing the cold air to blow. This can be caused by low refrigerant levels, a dirty air filter, or a problem with the blower fan. If the evaporator coil is completely frozen, it will need to thaw out before the system can function properly again.
In some cases, you may be able to fix this issue yourself by replacing the air filter or cleaning the coil. However, if the problem persists or you're not comfortable working on the HVAC system, it's best to call a professional HVAC technician to diagnose and repair the issue.