Old English snaw "snow, that which falls as snow; a fall of snow; a snowstorm," from Proto-Germanic *snaiwaz (source also of Old Saxon and Old High German sneo, Old Frisian and Middle Low German sne, Middle Dutch snee, Dutch sneeuw, German Schnee, Old Norse snjor, Gothic snaiws "snow"), from PIE root *sniegwh- "snow; to snow" (source also of Greek nipha, Latin nix (genitive nivis), Old Irish snechta, Irish sneachd, Welsh nyf, Lithuanian sniegas, Old Prussian snaygis, Old Church Slavonic snegu, Russian snieg', Slovak sneh "snow"). The cognate in Sanskrit, snihyati, came to mean "he gets wet." As slang for "cocaine" it is attested from 1914.
Old English storm "violent disturbance of the atmosphere, tempest; onrush, attack, tumult; disturbance," from Proto-Germanic *sturmaz "storm" (source also of Old Norse stormr, Old Saxon, Middle Low German, Middle Dutch, Dutch storm, Old High German sturm, German Sturm), from PIE *stur-mo-, from root *(s)twer- (1) "to turn, whirl." Old French estour "onset, tumult," Italian stormo "a fight" are Germanic loan-words. Figurative (non-meteorological) sense was in late Old English.
Storm-wind is from 1798. Storm-door first recorded 1872; storm-water is from 1847; storm-window is attested from 1824. Storm surge attested from 1872. Adverbial phrase _______ up a storm is from 1946.
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<a href="https://www.etymonline.com/word/snowfall">Etymology of snowfall by etymonline</a>
Harper, D. (n.d.). Etymology of snowfall. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/snowfall