See my trip reports for 2 other summits in this area: Saddle Mtn. and Duplex Summit.
There are two ways to get up to Dow Mountain - a long drive on gravel roads, or a forest road walk of around 2.5 miles (1900' elevation gain). Since I was also visiting two other summits along the way, I opted for the road approaching from the north. The road going up to Dow Mtn. from Hoodsport is gated - this is the road to take if you wish to hike it.