When cotton gets wet, it stays wet. I dress in layers, so I can regulate temperature throughout the ride. As it warms up, I can remove a layer, and when it starts to cool down again when the sun goes down, I can start adding clothes again. Zippers are another essential for temperature regulation. Turtlenecks with zip fronts and jackets with pit zips can allow a rider to be comfortable through a varied range of temperatures.
Silk is a natural fiber with great insulating properties.
It makes a great base layer. I often use silk for glove and sock liners. There are lots of synthetics available that wick moisture away from the skin and dry quickly. Polar fleece is another great fabric for winter sports. There is also bipolar fleece, which combines too layers to provide additional warmth and wind protection.