"Has anyone else experienced a severe storm while camping?"
Many, many times! Never terrified though... always fascinated at it! That's why we keep insurance on the trailer. Actually, thunderstorms, even violent ones, are a part of nature. I think it's equally important to experience the rain as much as the sunshine!
We've been camping on at least 3 different occasions when tornados were in the immediate area. The first, we were in our pop-up. Like you, we were under a heavy wooded area, and the trees broke all the high wind. The pop-up sides shook a little, but no so violent anything even came close to breaking. I thought the experience was exhilarating!
Another time, in our DutchmenSport TT, a tornado came thorugh and the winds were incredible. We were caught outside and the dust and fine particle of dirt, leaves, small twigs picked up in the wind were hitting us like a zillion ice picks stabbing us all at the same time. It hurt and stung. We ended up in a concrete shower house with a bunch of other people and everyone's pets (including our dog). Everyone was freeking out! My wife and I had a blast! We laughed, joked, looked out the door, and our antics actually helped put everyone else at ease. We kept reminding everyone that our camper was insured, as I was sure there's was too, we were safe, and if their campers blew away, it was a great opportunity to purchase a brand new camper! Somehow, I think, before we left that shower house, everyone actually WANTED their campers to get blown away!
Another time we at Port St. Joe State Park in Florida. A water spout was just off the peninsula heading for the town of St Joe. But we were behind the sand dunes and the brunt of the wind blew over the top of us. Next morning, the place looked like this. We made the best of it, and just enjoyed what Mother Nature threw at us.



We sleep in our camper almost every night at home (driveway camp). We stay in the camper during some of the most horrific thunderstorms. Our trailer is parked facing West to East. We get 35-55 mph winds where we live (on a sunny day), so the winds hit the front of the camper, just like when traveling down the road. We've never felt uncomfortable or uneasy. Thunderstorms are simply awesome when your right there in them.