How does air within winter clothing keep you warm on cold winter days?

Answer 1

Air is a good insulator and keeps the body heat inside and thus helps us bear the external cold better.

Answer 2

Your body is a heat source and therefore can warm the air between you and the outside, at the same time, the cold outside air will try to "chill" the air rather than your body. It's an insulating property (and air is not that good of an insulator).

Answer 3

All forms of insulation use trapped air to slow the dissipation of heat transfer. If you have many layers of clothing on it traps more air and as the outer layers of air cool to the ambient temperature your body heat is keeping the inner layers of air warm.

If you had one layer of trapped air as insulation and it was cooled then you would be cold, but with several layers the coldest layer is never near your body and you don't have to expend as much body heat to maintain your core body temperature.