Looking into this hike we found two Green Mountains in the area, one off Middle Fork and one in Kitsap County.  We wanted to try the one on Middle Fork / Snoqualmie Road.A bit hard to find: drive past MailBox trail for several miles until you come to a small concrete bridge.  Park on the side of the road before the bridge. Cross the bridge on foot and at the very end of the bridge on the left hand side you will see what looks like a game trail. There is no trailhead and no facilities here.  The trail looks like a boot path but you can tell it has seen use.  The area is quite nice, large old growth trees, birds and no other people.  Cross a couple of forest service roads (on the second one, follow it and it turns back into a trail again after a mile or so). Found a nice waterfall hidden deep in the forest, so we ended up coming back to it for lunch before heading back.  Running down wasn't too bad, some flat sections that we had to walk.  The trail was really more of a mud-pit in some sections. We really want to try this one in the spring or summer when the trail is more dry.