A violent wind; a tempest. Thus, 'a storm of wind' is correct language as the proper sense of the word is rushing, violence. It has primarily no reference to a fall of rain or snow; but, as a violent wind is often attended with rain or snow, the word storm has come to be used, most improperly, for a fall of rain or snow without wind.--Webster.
TO STORM
To blow with violence; impersonally, as, it storms.--Webster. We use it improperly in the sense of to rain or to snow.