1. As you increase in elevation, there is less air above you thus the pressure decreases. As the pressure decreases, air molecules spread out further (i.e. air expands) and the temperature decreases. If the humidity is at 100 percent (because it's snowing), the temperature decreases more slowly with height.
2. Unequal heating of the Earth's surface also forms large global wind patterns. In area near the equator, the sun is almost directly overhead for most of the year. Warm air rises at the equator and moves toward the poles. At the poles, the cooler air sinks and moves back toward the equator.
3. In general, colder air have greater density. It means that have bigger energy. In addition, rain usually means that is an air before the rain and during the rain is colder. So both affect in some way to wind production.