Green Mountain can be accessed by trail 110 (open to OHV and bicycles) from the west or southeast, or by bushwhacking from a spur off Spring Creek Road, SE of Orr Creek Sno-Park. The spur is narrowed by overgrown brush and trees, and the last 500' are deeply rutted, requiring a high-clearance vehicle. Deadfall across the road is likely, as this road seems mostly unused. There's a nice place to camp with a stone fire ring off a righthand spur toward the end of the road.
Bushwacking is the shortest option, and I found the NE ridgeline to be a fairly open moderate grade with a 500' ascent over 0.65 miles.
The activation zone is large and partially forested with many options for antennas and shaded activation spots.
This summit could be combined with others in the area: Gray-Line Summit (W7W/LC-033) and East Canyon Ridge (W7W/LC-034) being the closest.
Cat Creek Campground is nearby in a beautiful location next to the Cispus River. There are also numerous options for dispersed/free camping in the area.