Chiefland RV Park, Southern Comfort RV, Old Town Retreat and Suwannee River Hideaway make no mention of being closed in the summer and indeed look like successful busy campgrounds. I called Chiefland RV Park and talked to the lady and she said she did bot know of ant parks that close in the summer and that they are pretty busy with family campers in the summer especially since they added a pool.
I could find no mention on Passport of any campgrounds closed in the summer.
You still have not provided any names of any that close.