Do people with colorblindness have less cones or no cones of a certain type?
This is a complicated case, as it can have multiple causes.
The genes which are coding for the long (L, yellow) and medium (M, green) wavelength photopigments are located head-to-tail on the X chromosome. This is the reason why this colors are affected much more and especially in men (which only have one copy of this chromosome).

What seems to happen mostly is that the photopigment of one type of cone cells (and their neuronal connectivity) is missing, while the density of the cone cells is still the same. This means that the cells are they, but are not functioning. See these publications (when you have problems getting the articles, let me know in the comments, I can help):


The density of cones in the fovea centralis of the human dichromat
Color-deficient cone mosaics associated with Xq28 opsin mutations: a
stop codon versus gene deletions.
Functional photoreceptor loss revealed with adaptive optics: an
alternate cause of color blindness.


What can additionally happen in some cases is that these cones have a different pigment than they should have. See the third paper above for details.