I don't know any empirically based studies, but I do know personally that I have only once been aware of a colour in my dreams...a very vivid red. Perhaps more bizarrely I am much more aware of odours in my dreams, and garlic-y smells have cropped up more than once. Perhaps it was something I had eaten!
Colour wherever you find it is important. The brightest dreams -technicolour- promise the happiest times ahead. Colour is the music of your dream story as much as of waking. In specific circumstances colours in your dreams may be inverted i.e. what the dream projected as green may be red in waking life. So beware.
This is not a simple matter. High and bright colours suggest a happy day ahead, good feelings. (Dreams are the blueprint of waking experience) Dark scenes, black and white, promos dreary times. Often colours in a dream object turn out to be the opposite in waking. Colours are symbolical both in dreams and waking.