The National Weather Service said the first storm system is expected to arrive in the area Sunday night with light accumulation, and the second system will push through Monday and continue into Tuesday.
The storm's broad nature will bring snow, ice and slippery travel to much of the Northeast during the same time frame.
Cities along the Washington-Oregon border near Portland are within the zones that may get more than three feet of snow in total.
Palmer agrees with Mass on next week's possible storm, calling for a "potentially significant" snow storm Monday afternoon through Tuesday, with "major accumulation".
The advisory is expected to go into effect midnight tonight until noon Sunday.More news: Game modes for the Fortnite 'Share the Love' Series have been leaked
With temperatures already in the teens or single digits, meteorologists predict low temperature records could be broken on Sunday.
The weather service says that was colder than the Arctic coast or North Slope of Alaska.
In Tacoma, hundreds of people turned out for a snowball fight in a park after someone who lives nearby suggested it on Facebook.
Northern suburbs and northwestern suburbs stand the greatest chance of getting maybe 1 to 2 inches of snow.
Another was pictured walking along the waterfront in Seattle, with what looked like a solid wall of white behind her.More news: Order in which you drink booze makes no difference to your hangover
The National Weather Service said additional snow could fall Saturday, and another storm was expected early next week.
Many businesses closed early so workers could get home.
State and local officials urged people to stay off the roads over the weekend as traffic slowed to a standstill in some places because of the snow. In the central part of the state, snow drifts blocked roads and forced the closure of USA 2 and Interstate 90, in addition to causing multiple auto crashes.
In Portland, a tanker truck slid into a sport-utility vehicle on an interchange between Interstates 5 and 84 on Saturday, blocking the ramp for hours.
About 200 flights were cancelled at Seattle-Tacoma and Portland global airports Saturday, roughly matching the number of Friday cancellations.More news: Barrie’s jobless rate rises slightly, remains below provincial average: Statistics Canada
Seattle Weather Blog reports that Seattle woke up Saturday to its biggest February storm since 1962.