Home experiment.

Hold you hand in front of your face. Open your mouth as wide as possible and breathe on your fingers. Does it feel hot, cold or neutral?

Repeat, but close your mouth as narrow as possible so breathing is a tightly focused flow. Does it feel hot, cold or netural?

Other important considerations. Your internal body temperature is ~37°C, but your outer skin temperature is closer to 20°C.

When standing still you have an insulating layer of air around you. Your body is wanting to push out excess heat to prevent cooking itself. It loses that heat by radiating it, or by convection where some carrier rubs over your skin and carries away "heat". If the air is not moving, you have transferred as much heat away as possible and the air in immediate contact with you is saturated with heat. Example: hiding under the bed covers or wearing clothes.

Wind moving over your skin is transferring heat by convection. It is picking up heat from your body and carrying it away, which makes your outer skin feel cooler.