Minor problem with your theory. First of all, you have to keep in mind that the air inside the container is under high pressures and normal temperatures, forcing the air to turn into a liquid. Since your going against the natualr order of matter phasing ( Solid to liquid to gas – which is an energy releasing process therefore exothermic which is why steam is so hot)
So if going with the flow of natural phase shifting, you will lose heat, since exothermic processes is preferred (matter doesn’t like storing energy); so as you can tell from the
PHASE DIAGRAM for water, at room temperature (293 K) and just below one atmosphere (1 atmosphere equals 33 feet above sea level), you can see that air is in its natural form or vapor.
But if you force air into a can and compress it, you raise the pressure. So along the x-axis, go to 293 Kelvin and slide your finger up the chart and see what happens. It turns to a liquid, Which is what happens to air inside a compressed can. That’s why if you swish it around you can hear something inside. Now, again, making matter go against the phase change you increase the energy, making it endothermic. You are putting energy into the air.
Have you ever felt Liquid nitrogen or touched Dry ice? (I highly advise against it) It is cold. That’s because by forcing matter to go against the phase procession, you make it cold.
Basically what I’m saying is that in order for air to remove heat from your body, it has to be under compression and going against the phase change. Since there is no way air can be compressed in the open environment (open environment is the exact opposite of compression), could remove heat from your body.
The air needs to be cold to remove body heat even then it has to be freezing temperatures before it has any visible effect on the human body. Simply not attainable by an airbender anywhere but the arctic. The factors needed to chill the air to the point in which is can remove body heat is outside the scope of an airbender so as we have seen.
Oh.. and for the whole “Concentrated Stream” thing… Micro seconds after the cold compressed air escapes (turning from liquid to gas) it instantly heats up because its losing energy to air.
Basicly.. scientifically, anywhere short of the arctic caps, Air removing body heat and freezing a person is impossible because the conditions to make the air at a state to cause damage (high pressure and controlled temperature), are unattainable. There is no way the avatar could pressurize the air above your skin equal to 14700 PSI (Psi at 10^3 atm), there is no way that he could manipulate the air to be able to freeze you.
The only way to die from wind freezing you is in the arctic, which the air is cold due to the amount of ice surrounding it. Otherwise, in an area like the Earth Kingdom or in the Fire Nation, the ability to use air to suck heat out of the body is impossible, for the air has to be significantly colder than the human body.