Wool vs. Cotton
Let's do an experiment to see how cotton and wool are behaving when it gets wet. Here is one ball with raw cotton and one ball with raw wool. If we soak them in water and squeeze them, we can see the wool fibers will rise back to its original shape, and the cotton fibers will collapse. While the wool fibers rise back to its original shape, it will still insulate and dries faster. Cotton will not insulate, and it dries slower.
What we can conclude with? Its just as important to have wool in your boxers as your socks. Get rid of all cotton next to your skin if you want to stay warm and comfortable.