Cotton fails even in hot weather. Try a cotton tee shirt soaked with sweat and then a wicking polyester tee. The polyester tee will wick away the sweat and dry quickly and is FAR more comfortable. A soaked cotton tee is just heavy and soggy. If the sweat isn't evaporating, it isn't cooling.
Polypropylene is outdated. It was found that most of the wicking ability of polypro was due to oils used in manufacturing process. Once those oils are removed after repeated launderings, the wicking capability falls off. Polypro suffers from odor retention and can be easily damaged in a dryer. The polyester fabrics used by the better outdoor clothing manufacturers are superior. I personally use base layers made by GoLite and Patagonia.
I like cotton for casual wear, but when it comes to hard hiking and maximum benefit to weight, I'm wearing synthetics.