There is a campground on Highway 10 / 90 / Lafyaette Street, at Mariana, Florida that has the same policy, no electric heaters. When we were at Florida Caverns State Park over Christmas (2015), and we were being told we might have to evacuate because of flooding, we checked out this campground since it was so close to the State Park we could spend the rest of our week there.
Well, when we read the rules about no Electric heat, we were a bit taken back on that. So, when it DID finally happen, and we did have to evacuate, rather than going there, we just headed for home. We actually stopped at another campground about half way home that still had full hook-ups and water (in December) and stayed there a couple more days.
So yea. I personally would not stay in a campground that would not let us run air or electric heat! My camper will turn into an oven on broil without air! I couldn't even stay in it.
My suggestion ... find another park... BUT! Be sure to tell them why you're not going there! I did tell them at that park in Mariana. The guy just looked at me like, ... "Oh well ... it's your choice ... someone else will camp here!" ... well ... maybe so, but it won't be ME!