Better start packing up then! See this: http://cliffmass.blogspot.com/2012/12/does-it-really-rain-al...
The relentless gray of which you speak is true of months like December and January.
I'll also take nonstop rain from Nov-Feb any day over the snowy winters in the Midwestern states where I grew up.
Finally, the key to not letting your plans get ruined by rain is to always plan for the possibility of rain. =)
When I travel, I always emphasize the rain, the cloud cover, the risk of death by volcano, the very real likelihood very overdue The Big One earthquake, how traffic sucks, etc.
http://en.wikipedia.org/wiki/Emmett_Watson http://en.wikipedia.org/wiki/Lesser_Seattle
That said, sometimes it does rain a lot in Seattle. Some years ago there was a stretch of 35 consecutive days of rain.