Wool does insulate better than cotton when both are wet. The reason has less to do with the amount of water than with the type of fiber. Cotton fibers are solid bit of cellulose. When they get wet, the fiber is wet all the way through from one side to the other.

Wool fibers aren't solid. They have numerous pockets of air inside them. When a wool garment is wet, it is wet between the fibers but not wet in the fiber. The inside of the fiber maintains the air pockets and their insulating quality. The garment will still feel cool but it won't be sucking heat away from your body like it does with cotton.

Man-made fabric share some of the same qualities with wool. The fibers may not have as many holes in them to provide insulation but they don't wet the same way as cotton does. Your body heat drives the moisture towards the outside of the fabric and the water doesn't absorb into the fabric so it maintains its insulating quality.

None of these fabrics work all that well if they have wind blowing across or through them. A wind barrier is as important if not more so than the insulating layer. While your body heat will drive that moisture in wool and synthetic fabrics towards the outside of the garment, that moisture carries a lot of heat with it. When it evaporates, you are losing that heat and have to make it up. A wind barrier layer may make you wet and a bit clammy but that's better than being wet and cold.