Why sometimes it's too cold to blow out the air conditioner, sometimes it's a little warm, but my mouth gets angry?

This is closely related to air relative humidity and air pollution index.

In sunny and cold weather, the relative humidity of the air is small and there are few pollutants. The breath blown out cannot condense into water drops because there are few condensation nuclei. Even if it condenses into water droplets, it will evaporate quickly, so you can't see the breath.

The weather is cold, the air relative humidity is high, and there are many pollutants. The breath blown out has enough condensation nuclei to condense into water droplets, and because the air vapor is close to saturation, the water droplets are not easy to evaporate into water vapor, so the form of breath is formed.

I hope it helps you!