Some monsoon clouds in India - Cirrus, Cumulus, etc. - are white because of Mie scattering. But the rain-bearing monsoon clouds - Cumulonimbus, Nimbostratus - are dark (different shades of black and grey).
I assume you are talking about the visual appearance of clouds, as they are observed by individuals from the Earth's surface during daytime. In that case, the darkness of clouds is a very strong function of their depth and water content, as well as the geometry of illumination and observation.
The darker the cloud appears, the fewer photons are reaching your eye. So you need to think of all the processes that attenuate light propagation (initially coming from the Sun) in the direction of observation. These include Rayleigh scattering outside of the cloud, Mie scattering on small droplets within the cloud, refraction of light by droplets (creating rainbows and halos, which are dispersing light in specific directions), absorption within the water droplets, etc.
The same cloud will look (1) very bright when seen from an airplane (i.e., from the top), especially when the phase angle (the angle between the incoming direction from the Sun and the outgoing direction to the observer) is close to 180 degrees, and (2) possibly very dark when looked at from under the cloud, when photons have had ample opportunities to be scattered in other directions or absorbed. Again, if you look at a satellite image, there are no dark clouds...
Many thanks for your long and informative response.
I still do not understand why the rain-bearing clouds, even when these are very thin and very low, are dark, whereas huge Cumulus clouds are white. In India (be it Kolkata or Kanpur, where I have lived/live), immediately before heavy Monsoon rains, one sees very thin, very low, tiny (area-wise), very dark, clouds, which move with a higher speed than the other grey/dark clouds. These (so-called menacing clouds) announce that heavy monsoon rains cannot be far behind. One can see other clouds above these clouds, which are thicker, larger (in area), and less dark. The rain-clouds have obviously much higher H2O content, but H2O absorbs in the infra-red, but not much in the visible spectrum.
My guess is that the dark clouds contain a much higher concentration of dust particles, at which water vapour nucleates (vapour to liquid/solid phase transformation); these dust particles absorb in the visible range.
Thank you Neeraj for your response. What Michel and you have written can apply to high monumental clouds. What about the very thin low lying clouds of small areas (few hundred feet by few hundred feet) which fleet past you and often rain as these go over you. I wonder whether you have experienced these clouds rain over you when they are over you for a short time as these move at much higher speed than the other clouds during rain time. These thin clouds are grey and can be almost black also. These are called menacing clouds; these announce imminent long duration rain by the other clouds. Rain to me is beautiful when in India in summer; I wonder why they are called menacing - perhaps by the people from UK, where rain means very different from what it means to us.