It is advised by many fasting gurus that during a Water Fast it is essential for our body to rest to conserve our resources of fuel. During the fast your body starts to use fat as energy. If you exercise it quickly uses up that energy and taps in to the protein reserves.
If you want to light work, light walking or Yoga that is fine, if you are able to do it. After a few days of fasting it will be harder to do any strenuous work or exercise.
Best results are gained if you rest, stay warm, drink as per thirst and have no mental stress.