Don't know about swimming in the lake, but you can bring a pop up trailer and bbq if you wanted to do so.
I think its not allowed to swim on the lake, besides the is only open on weekends until 5pm. Trailer and bbq are good just make sure you booked for the campsite before going there.
Not sure about the lake. We had class C RV, popup should be fine, full and partial hookups. We had gas grill, bbq should be fine.
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