It’s because the ice crystals in the clouds scatter the light from the sun in all different directions. This means that light of lots of different wavelengths gets mixed together so you see white light. Have you ever tried spinning a colour wheel really fast? When all the colours get mixed up you just see white (see http://www.youtube.com/watch?v=ZUlRH5ouBrY&feature=related). This is what happens in clouds.
When you see grey clouds it’s because there are higher clouds casting a shadow.
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