It turns out, our window is still open for a little while longer. The latest snow was on April 17 in 1972, when 1.2 inches of snow fell at Sea-Tac Airport. Not much, but enough to at least piece together a snowman or two.
And just two years ago, it snowed a little on the first day of spring (March 20, then), so it's not unheard of. Although long range forecast models don't offer much hope for any more snow this winter.
Already hoping for next year? The earliest snow was, coincidentally, the same winter season as the latest snow -- coming Oct. 27 in 1971. There, Seattle got about 2 inches of snow.