I rode a rigid mountain bike when I lived in true snow country in the late 80's and 90's just a few hours drive east of the OP. (UP of Michigan)
In the Pac NW I don't see too much snow on the roads, but it sometimes happens. Got some Nokians for the 'cross bike for this winter for the few days of icy, frozen roads if we get them.
Here's some Pacific Northwest snow bike pics from 3 different snow tours. All of a Long Haul Trucker