Why is that my face often sweat, but in air condition environment it does not .

Low humidity: A/C reduces the humidity in the air which makes your sweat evaporate without a trace . The cooling also makes you less likely to sweat which is the mechanism by which by the body loses its excess heat. For example, one may not even sweat at all when the humidity is below 20% and the temperature over 100 F outdoors .

Sweating: Sweating about the forehead can be caused by heat intolerance, anxiety or stress. Generalized sweating may be a sign of fever or overactive thyroid. Sweating in the back of the head without other causes can be seen with certain malignancies. Since you're ok in air conditioning, I doubt that you have any serious health problems.