Steady rain is about to turn to showers as a cold front pushes through the area. Colder air follows in waves. The first wave drops the snow level to 1,000 feet Saturday, but moisture will be scarce, so we're looking at scattered rain and snow showers and sunbreaks with valley highs in the low 40s.
Sunday brings another wave of colder air, with the snow level between sea level and 500 feet, but again, we're only looking at scattered snow showers and sunbreaks. Monday brings even colder air in but a sunny windy day as east winds kick in. The clouds increase Tuesday as a surge of Pacific moisture approached from the west. Depending on how much cold air has filtered into the Willamette Valley by then, when the precipitation begins early Wednesday morning, it will likely fall as snow. There's also a chance it may be freezing rain in Portland and snow farther north, say up near Seattle.
Worst case scenario is several inches of snow falls followed by a changeover to freezing rain Wednesday. Temperatures will gradually climb above freezing Wednesday night and Thursday.
Best case scenario is Portland ends up with just a cold rain. At this point I think it's likely that some parts of the Northwest lowlands will see snow, potentially heavy.