Breath is released from your body at 37.5 C 

The temperature outside your skin is normally lesser than that. So, the skin ought to feel warmer when you breathe on it. So why does it feel colder when you "blow" instead of "breathing"?

I thought a lot, and I can come up with two hypothesis.

1) There may be some perspiration/sweat/moisture on your skin, which evapourates when you blow on it. This makes it colder. This is similar to the effect of a hot wind. Even though the wind is hot, if it evapourates sweat efficiently, the net of the two effects may cool the skin. 

2) The second reason is linked with human evolution. Wind has almost always been dangerous for cave-men. If you are out in the cold wind, there is a considerably increased chance of you dying out of cold. 

The body recognises this, and we have evolved mechanisms to recognise pressure on our skin as wind. The brain exaggerates the cooling affect of air on the body if it applies considerable pressure on the skin, and tells us that this can be dangerous.

3) There may be another reason. There is always a warm insulating layer of air near our skin. The wind removes this layer, hence exposing the skin to the colder air outside. Even if the air we blow is warm, after it passes the body, it brings in the cool air from outside. 

Student in Electrical Engineering, Indian Institute of Technology, Kharagpur