More general discussion of this can be found at http://www.urbanlegends.com/language/eskimo_words_for_snow.html and http://www.public.iastate.edu/~honeyl/derrida/eskimos.html
The average English dialect has just as many words for snow as the average Inuktitut dialect. After spending about ten minutes with Google, I found these root words for "frozen precipitation":
The list increases dramatically if skiers' technical terms (pack, powder, etc) or the many slang terms for cocaine are included.
The urban legend in question derives from the agglutinative nature of the Inuktitut language; because the definition of what makes a word and what doesn't is a little foggy, compound words (compare English snowball, snowflake, snowstorm, snowblind, snowfall, snowman, snowdrift, snowplow, etc.) get counted and over-counted.
On the other hand, English has numerous words for mud, more distinct than the snow roots; see http://www.alt-usage-english.org/ucle/ucle9.html