You can really wander at Cougar Mountain, and that's what I did today for my trail run. Ended up touching quite a few of the trails over the course of 7.5 miles and wound up with a total gain of almost 1,200 feet. Incredible area for trail running, and the majority of other people I saw out today were also running. Didn't bump into a ton of people until the Cave Hole Trail.
I decided to make up my route as I went along today, and for the most part it turned out great. The only regret I have is using the Belevedere Loop, which spit me out into the street below the park entrance, so I had to run the last half mile up the road to get back to my car. Other than that, great network of trails to explore.
There was a bit of mud in places that you'll need to leap over or circumvent, but none of these patches was too nasty. Highly recommend this park for trail running--you can really get some varied terrain.