The Inuktitut for snow in general is aput.

I don't really know what 'polysynthetic' was meant to mean. It's not a term I or (I think) any modern linguist would use. Inuktitut is agglutinative, and synthetic, but the word-formation is not hugely different from that of any other such, like Turkish, as far as I know.

The Urban Legends site discusses this at
http://www.urbanlegends.com/language/eskimo_words_for_snow_derby.html.