Why do our hands seem to become "wrinkled" after a long bath or after a swim?
because the water enters your skin.
The only responsible of this wrinkled appearance is the callus on your skin. Hence, if you want to prolonge your bath for more than half an hour, you may experience the wrinkled hands and feet.
You may be interested why the hands and feet are more wrinkled than the other parts of your body. This thing happens because your hands and feet do most of the physical activities. Hence, the more you walk, the thicker layer of callus will be generated by your skin.
Since the callus does not reject the water, the more it is imersed in water, the more swelled the callus will become. These swells will create the wrinkled aspect that you can see when after the long bath.