Just what the title states; and this isn't an original question:
On full-moon, moonlight is almost as bright as mid-dawn; yet there is hardly any colour visible. This is not the case with sunlight.
I'm curious to know why this is the case.
Moonlight is not almost as bright as mid-dawn. Moonlight is really fairly low illumination, and human eyes don't detect color well in low illumination.
Moonlight is reflected sunlight. If there's enough of it, it produces color mostly the same way sunlight does. This page, found through a Google search, shows a spectrum of moonlight. All the colors are there. There simply isn't enough moonlight for our eyes to detect color well.
See http://en.wikipedia.org/wiki/Lux
The "dark limit of civil twilight" corresponds to ten times as much luminous power per unit area as a full moon. If you look at the Wikipedia article for what counts as twilight, the pictures there aren't very colorful.
'Color' is just the human minds way of interpreting wavelength. Your eyes have two types of receptors. Without going into too much detail, one (rods) 'sees' intensity and the other (cones) 'sees' intensity and wavelength - that is, color. The rods are more sensitive than the cones. Below certain intensity the cones ability to detect color simply doesn't work. Moonlight falls well above the rods ability to see, but below the cones ability to register wavelength. In other words, you are color blind in low light. But the colors are still there.
Stepping down in luminosity, go from the outdoors in sunlight, move indoors to a room with the light on, then step outside into you front yard with a full moon. In each of these cases, even though eventually the environment seems quite bright, it still takes time for your eyes to adapt to the lower light levels.
I have seen moonlit nights here (Australia) where some colours, mainly in the green areas of the spectrum, are almost clear; the amount of light in the environment however is still much lower than is available at dawn. And of course in low light conditions our eyes loose the ability to distinguish colours as the cells in play (the cones) need a high level of light to work; the cells that work in low light (the rods) only see greys.