A 2009 blog post from the New York Times says the term is Western Washington's own, first appearing in 2006 and snowballing (ahem) from there:
"Snowpocalypse” appears to have made its way into the vernacular; ABC News even used the term in a Web headline on Saturday. However, the word might be more familiar to those in the Pacific Northwest. Urban Dictionary suggests the term emerged in Seattle in late 2008 to describe a Dec. 20 blizzard. But the term seems a bit older than that... our adventure in Google etymology yielded uses of the term in 2007 and even 2006 – both those years apparently referring to northern Washington State storms as well.
That cited 2006 blog post—by one "snickerpants"—claims that the blogger's husband coined the term:
The denizens of the Seattle area are not used to snow. This results in an entire Metropolitan community being physically unable to cope with lots of snow in a short amount of time. In rare circumstances this results in something my husband has termed a “Snopocalypse.”
HOWEVER! I found a 2005 usage on the now-defunct Seattle MetBlog site. So even if the husband independently invented the term, it has older origins. And I'm guessing the word is as old as jokes.