In a cold climate, do people often blow out the air from their lungs a lot when living in the cold condition to keep their lungs warm?
No, and it wouldn't make any sense: breathing more means inhaling more cold air that needs to be warmed up, so the result is a heat loss. The more so, as cold air (< 0°C) has a low water vapor pressure, while the lung likes to have the air at body temperature and well moistened. Which means that you also loose the vaporization heat of the water.
The function of moistening and heating the cold and dry air as well as recollecting some of the heat and water when breathing out is done by the nose. So the sensible (and done) thing in cold weather is to avoid breathing by mouth and instead keep your mouth shut and breathe by nose.
Nevertheless, neither German nor English, nor any of the Scandinavian Germanic languages is spoken through the nose.
My experience is that cold air (personal minimum: -40 °C) in the mouth is very unpleasant, and makes me cough as it is still cold when it arrives in the throat, but of course breathing out by mouth is less of a problem. But breathing out by mouth and in by nose means that the nose cannot recollect the heat and moisture from the outgoing air.
In any case, the amount of breathing is linked rather to oxygen demand and $CO_2$ to be gotten rid of), and even the fastest speaking people I know do not get close to hyperventilation by speaking, not even speaking German or English.
Which means that speaking Germanic languages needs less breath to produce the sounds than what you need to breathe for physilogical reasons even at not much above base rate metabolism (sitting while talking) anyways. Which would imply that the breathing difference between Germanic and Sino-Tibetan languages would not cause an important driving force in language evolution.
A side point is that I don't agree with your concept of cold climate. Both Germany and England are counted as temperate climate. Actually, Frankfurt has higher minimum temperature all year round than Lhasa (as you mentioned Tibetan in your language family).
Also note that the Indo-Germanic language family covers a range of climates from tropic to polar just as the Sino-Tibetan covers some cold regions as well), so maybe language families that are spoken only in polar regions vs. such that are spoken only in tropic regions would be better to look at (see e.g. the Wikipedia language family map).
However, there are probably some confounding influences that need to be taken into account. In cold weather, you do not sit or stand around chatting with people as much. And in the polar climates, historically farming has hardly been possible. So you have populations where hunting has been very important for survival, and regions with very low population density. Both mean that on average, you'll be silent instead of talking. As for having a chat with someone, you'd ask them in - or the length of the chat is limited by temperature.
Which means that if cold is a driving force for the type of pronouciation that evolves, it would be a rather weak link. And in any case, speaking less will overcompensate all these breathing differences.