You sweat because your body is overheated..period. If what ever you are wearing gets soaked, you have too much on.
The problem if you can overheat for 200 feet and froze after. an overheat again.
I was waiting at athe bottom of a route that my partner belay me, it was very cold. When I began to climb, I used a lot of eenergy. All the cold blood of my arms was going to the heart and brain, creating a mild hypothermia: sick, shivering, finger too cold, etc..