I know Ideal dips their chicks in food coloring, which is pretty harmless. I see nothing wrong with the dying of animals . . . it's the selling of dyed animals I object to.
Sometimes I dye my animals for no particular reason. I drop a few drops of food coloring on and comb or rub it in. It gives a mottled look, not a solid one, but I think it looks better because I can make swirls of different colors, polka dots stripes, etc. It only stays for a week since I just use those cheap little coloring bottles you can get in any grocery store, but honestly if it lasted any longer I'd never do it. It holds the same appeal for me that doodling on my skin does . . . it's more interesting to write on than plain old paper, but I want to be able to wash it out because I like my skin in its natural form.