Christians in NC
If memory serves me correctly, the park closes at sundown. The hiking trails are closed after dark, but all three of us had hiked the trail before and were comfortable doing it in the dark or with dimmed flashlights. As soon as we left the campsite, we stripped down. The trail traversed a country road at one point, and we snuck from tree to tree closer to the crossing, waiting until we didn't hear any incoming traffic before scampering across.
I'm big enough that my thighs were rubbing together, and the next day I could hardly walk; keep that in mind if doing any nude trekking.
As far as enjoying the sunshine nude, I would recommend going to the nearest national Forest. The trails are usually not busy, especially during the week, and the park rangers enforce federal laws, which do not include any impositions on nudity. You can call the rangers and ask for their policy. I free-hiked Uwharrie National Forest one evening last June for three hours, and didn't see a single person until I was driving away from the trailhead.