Yes, there is a nice separate gated section for small dogs, but most of them seem to like to play in the big dogs section.
There is a smaller gated area by the water fountains that's meant for smaller dogs or puppies, but I've never seen any dogs in there. Dogs of all sizes are usually in the (much) larger gated area.
No the park is not separated by small and big dogs. Yes the park is gated and the dogs are off leash.
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