Not necessarily true, most people dream in black and white, but not all. When I have lucid (dreams you control), and vivid (a dream that you can remember extremely well) dreams, they seem to be colour. But the majority of my dreams are in black and white; but I suppose you have a point. It would make sense if dreams were in black and white, but important aspects of the dream were in colour.
For those who care, writing down a few quick notes about the dream you had, as soon as you wake up; will increase your memory of dreams over time and eventually you will get lucid dreams more frequently
