Yep. The warmer the air, the more moisture it can hold. The colder, the less moisture the air can hold. You need moisture in the air for it to snow or rain. The temp difference also explains how you get dry powerdy snow vs. wet heavy sticky snow. The temperature at which such snow was made. Generally speaking, it wont snow below about 24 - 25 degrees F.
<---------------Was a meterology major for a while.
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