The Cove Lake Loop makes its way around the lake in the Cove Lake Recreation Area a couple miles north of Mt Magazine. The length is either 2.9 or 3.5 miles, depending on whether you take the longer route via Lookout Window (which I did). It appears in the upper right corner of this topo map.
The longer route requires a 300′ climb. The reward is a bit of a view to the south and west but not much of the lake. You can get basically the same view from 1200′ higher on Mt Magazine. Other than that, it’s a nice walk in the woods with a bit of wetland habitat thrown in.
The trail actually ends on the south side of the lake near the boat ramp. From there to the parking area at the northwest corner of the lake is a road walk through the rec area and across the dam, about .4 miles of the figures above.