I've only seen them in the residential and developed areas out there. Just because it's marked as a forest road, doesn't mean that it doesn't cross private property.
The 73 road is one example that comes to mind. Also the road to Ranger Creek Airport.
You will generally find No Shooting signs in the developed areas, in the lowlands, and I can't see why a Pierce County Ordinance wouldn't apply in Pierce County. I've never interpreted those signs to mean No Shooting all the way up into the hills.
As an aside, did you know that the Forest Service can only require a pass in developed areas, and they have specific definitions of what a Developed Area is? Must have a picnic table, regular garbage service, and a toilet. They often post the Pass Required signs in areas that don't meet those requirements.