There is about a mile of paved path to walk your dog if it is too muddy to let them run in the enclosure.
It's wet there alot there is a water pump and you could bring an old towel after you rinse the dog off
Best thing to do is not go if you're worried about it being muddy after a rain but you can stay away from the river area and walk closer to the playground area and dog park so you don't have to get near the flooded areas
It's almost always muddy or flooded for at least a couple days after any rain. You could still walk on the tracks though, they're paved.
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