Cotton grows in the colors of the rainbow.  I think that white cotton has been mostly monocropped by the big textile interests for quite a long time (since chemical dyes became reliable and standard, and white cotton has desirable features like long, strong fibers), but if you could get your hands on heirloom colored cottons, they're gorgeous!  Their fibers are evidently shorter and weaker than white cotton.

Here's an article on naturally colored cottons from the area of Peru where I lived and did research!

http://www.perunaturtex.com/scientif.htm

If you google "Sally Fox" and/or "naturally colored cotton" you will find a wealth of information on the stuff.  You can even buy seeds for naturally green and brown cottons, although green evidently doesn't retain its color as well as other naturally colored cottons.

http://www.localharvest.org/store/other-seeds.jsp?q=cotton

Some of these are natural tints, and the pictures are great:

http://www.mielkesfarm.com/cotton.htm

And here's a paper (which I have not finished reading) on color retention of such cottons when "refurbished" by selected (modern) laundry treatments (soaps, etc.):

http://cati.csufresno.edu/ip/rese/99/990901.pdf

Finally, here is a small list of varietal names for colored cotton seeds:

Arkansas Green Lint
Brown
Nankeen ( light brown)
Peruvian Brown
Sea Island
Texas Green Boll ( several shades of green)