Colour blindness comes in various forms. The most common is where the red cones are missing and the person only sees blue and green. They cannot see the colours that contain red. Green or blue cones can also be missing giving rise to other forms of colour blindness. It has little to do with our construction of colour except that the signals from those cone cells are transmitted to our brain in order to construct colours. Missing signals lead to missing colours.
Complete lack of cone cells, ie fully colour blind, is very rare but does occur and is quite debilitating as just having rod cells makes us far to sensitive to light. Oliver Sachs wrote a book on this called "The Island of the Colour Blind".
Cones are concentrated in the fovea, rods predominate in the periphery of our eyes.