The answer to 'why is my thermostat blowing cold air' is that your HVAC system is likely in cooling mode when you want it to be in heating mode. This can happen if the thermostat is not set properly or if there is an issue with the thermostat or the HVAC system.
Some common causes include: the thermostat is set to 'cool' instead of 'heat', the thermostat batteries are dead, the thermostat is malfunctioning, or there is an issue with the HVAC system itself like a refrigerant leak or problem with the heating element. Symptoms may include the system blowing cold air, the home not warming up, and the thermostat display showing a lower temperature than the actual room temperature.