We actually just got home from the Clayton park
It is completely fenced, both small and large areas - even the woods in the back of the large area are fenced around the back. There's one small gap between the two sections that our guys slip through now and then, and they can squeeze between the hinges on the gates (they're all in the 4.5-5lb range), but if you keep him more toward the back of the area, there's nowhere for him to escape to, and there's usually so much going on with other dogs, he'll be too distracted to want to go anywhere.
We've found of all the parks we've been to, this one tends to have the friendliest and most "dog-smart" dog people, and consequently some of the friendliest and most playful dogs, which makes it a great place to socialize your dog.
One important tip (channeling Cesar here), if your dog is cowering around your feet and wanting to be picked up... DON'T DO IT (unless he's in actual danger, of course) - he needs to learn to stand his own ground with other dogs. We ran into exactly this with Daisy when we first got her, and stuck to that advice... three days later we took her back by the store for a visit and they all said she wasn't even the same dog. Now she runs all over the park on her own.