c. 1300, from the noun, replacing Old English sniwan, which would have yielded modern snew (which existed as a parallel form until 17c. and, in Yorkshire, even later), from the root of snow (n.). The Old English verb is cognate with Middle Dutch sneuuwen, Dutch sneeuwen, Old Norse snjova, Swedish snöga.

Also þikke as snow þat snew,

Or al so hail þat stormes blew.

[Robert Mannyng of Brunne, transl. Wace's "Chronicle," c. 1330]

The figurative sense of "overwhelm; surround, cover, and imprison" (as deep snows can do to livestock) is 1880, American English, in phrase to snow (someone) under. Snow job "strong, persistent persuasion in a dubious cause" is World War II armed forces slang, probably from the same metaphoric image.

Old English snawhwit (glossing Latin niveus), from snow (n.) + white (adj.). Similar formation in Dutch sneeuwwit, Middle Low German snewhit, German schneeweiss, Old Norse snæhvitr, Swedish snöhvit, Danish snehvid. The fairy tale is so-called from 1885, translating German Schneewittchen in Grimm; the German name was used in English by 1858.