I never have seen anyone grilling, so I don't think so, I have see big picnics but no open fires.
I don't ever recall seeing anyone grilling in the park. If you were to do it you'd probably want to do it on the southern end, near the boat ramp; there would be less crowd since it is away from the play ground area.
You don't have to reserve to picnic or barbecue but it can be a busy place Friday thru Sunday, sometimes Monday thru brunch time. People in general are friendly and respectful.
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