Mud Mountain Dam is a U.S. Army Corps of Engineers flood control dam and recreation facility on the White River south of Enumclaw. Since the dam is only for flood control, it usually doesn't hold back much water except in times of high rainfall/runoff, leaving the riverbed trails high and dry much of the year.
From the equestrian parking lot, the River Trail winds down towards the river bed on a gravel road, then follows the river bed eastward upstream for a couple of miles. If the river is flooded, this may be as far as you can go, or if it was recently flooded, the trail may be indistinct and muddy. But eventually it pulls away from the river into the woods, and meets up with Scatter Creek, where there is a ford to continue following White River. Eventually you will have to turn around and ride back, though.
To the north, you can connect to the Mt. Baldy/Griffin Russell trails, but be aware that Hancock Forest Management requires a permit to access trails on their lands. Info
From Enumclaw, take Highway 410 east. In about 6 miles, turn right onto SE Mud Mountain Road. The equestrian parking lot is on the left after about 1/2 mile.
Park open weekdays during the winter, weekends as well during the summer; see website below for details. Trail accessible every day.
Length: 6.5 miles
Surface: gravel road, dirt and mud paths
Share with: hikers, bicycles
Down the road at the day use area there are restrooms and picnic facilities, but not at the equestrian parking area
Parking for: 6+ trailers
US Army Corps of Engineers:
http://www.nws.usace.army.mil/PublicMenu/Menu.cfm?sitename=MM&pagename=PAGE1