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" 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.