400mm, ISO500, 1/30,F5.6
Photography is all about the light. Digital images are simply a recording of the light reflected from the subject, through the lens, an onto the camera's sensor. The flat bright light present when the sun is high in the sky is the type of light most tourist snapshots are made with and for the most part it is the worst light of the day. On clear days good wildlife light can be over within a very short time after the sun rises above the horizon. Capturing good wildlife images on clear days requires being afield by first light and again in the late afternoon, staying until the last light of the day has faded. Unless you can find your subject in an evenly shaded area there is only a slim chance of making an image worth keeping.
Cloudy skies are a different matter entirely. The soft diffused light falls evenly across the subject muting highlights and filling in shadows allowing the capture of great subject detail. As an added bonus wildlife will typically remain active for longer periods of time.
Shooting under heavy skies does have one major drawback, the quantity on light. This can be overcome by shooting at high ISO but high ISO increases digital noise; those tiny red, green, and blue dots that destroy image quality. Lower shutter speed also counteract the lack of light but requires stationary subjects, and wildlife is notorious for not holding. The very best way to compensate is with fast lenses, lenses with an aperture of F2.8 or larger will do a fantastic job of letting in the light. Their major drawbacks are weight and size as well as taking a large bite out of your children's inheritance.
Even if fast lenses are not an option for you don't pass up the cloudy days. Experiment with your camera to find just how high an ISO your camera can handle while still capturing an acceptable image. Steady that camera on a good tripod and shoot lots of images; hoping to snap one while your wild subject remains still. Trash the blurred images, keep the sharp ones, and enjoy your cloudy days afield. Besides any day spent outdoors shooting wildlife is far better than being inside and you just may capture the most beautiful image of your life.