Well, it is not true that dogs see only in black and white. If, however, what you mean by colorblind is that dogs see only a portion of the visible spectrum as compared with what humans see, then yes, dogs are colorblind. Dogs do see colors differently than we do. Dogs don't seem to be able to see red and green very well, so they see the world probably in shades of yellow and blue. But first, it is important to understand how dogs see.

Dogs have two types of color photo reception, or cone cells, on their retinas that recognize short and medium-to-long wavelengths of light, corresponding to bluish hues (short wavelength) and red-yellow ones (long wavelengths). People, on the other hand, have three types of cone cells that enable us to see the full range of colors that make up the visible spectrum. Since dogs have only two types of cone cells, the colors they can distinguish are almost identical to the colors a human who has red-green color blindness would see. Of course, colorblind humans still see many different colors, and scientists think dogs see this range of colors as well.

As humans we tend to think of dog's visual capabilities as inferior to ours. It is different but it may suit their needs better than possessing accurate color vision would. Dogs can see in much dimmer light than humans and dogs can detect motion better than humans can.