If you let the air out gently, it comes out at about atmospheric pressure, and at the same temperature as your lungs, which in most times and most places is warmer than ambient. What is more, it is saturated, or supersaturated, with moisture, which gives up warmth on condensing.
However, if you blow hard through pursed lips, the air emerges at a pressure significantly higher than atmospheric. It expands abruptly as soon as it leaves your lips. This expansion amounts to doing work, the energy for which comes largely from the heat in the compressed air, and causes adiabatic cooling. It is in fact a simple example of part of the cooling mechanism used by most commercial refrigerators.
Incidentally, this is the basis of the expression "blow hot, blow cold", which as far as I know, originated with Aesop's fable of the man who blew hot and blew cold, thereby alarming his naive fellow-traveller.
Go well,
Jon