[akhtene]

I'm not sure, but maybe just common associations:
white - the purest colour, meaning the greatest fighter with evel (the one Saruman was supposed to be)
grey - that's for something/one obscure, like 'grey cardinal'(if that sounds right in English), the one who gives advice and teaches without claiming any obvious power; or grey can be the colour of road clothes and road dust, as Gandalf had to travel a lot. Unlike Saruman he didn't seem to have any permanent dwelling.
brown is just the colour of the forest.
blue - that's something mysterious, vanishing (vanish into the blue)