Never, never, NEVER, believe that sunburns only happen in the summer. We were college sophomore or juniors. It was early June and the water was not freezing.We were out in one of those small floating barge things, bigger than a kitchen table, smaller than a dining room table with barrels attached. I burned head to toe, luckily I was wearing a bathing suit. I was red, and pain is severely not fun. When I peeled, I looked like a moulting lizard. Lesson learned. That tan stayed around for months.
So, while I am all for skinny dipping, that day, the bathing suit saved my bottom and dangly parts.
My wife has had sun allergy problems in the past and wears a bathing suit at the hot springs. I don't, and I am also very likely to walk back to the car naked as far as I legally can. People on the trail to and from usually don't care. And the nice thing about our hot springs? Mostly in the shade. I have never again experienced a sunburn that covered that much territory, and I hope I never do it again.
So, sunscreen. Avoid the pain, avoid the skin cancer and avoid the bad memories.