godfather,
wood greys because it is being sun bleached, moisture is drawn out of the wood and the resultant oxidation. All wood will turn grey as ultraviolet radiation causes cellular damage on the surface of wood. If these damaged wood cells are not removed they become a food source for micro-fungi. As the fungal growth progresses, the wood becomes darker and eventually begins to rot.
For a weapon that is in use either as a weapon or tool, I would think that any paint or coloration would wear to the blonde color of the wood. (Ash, oak or some other hardwood being used for the haft.) Any subsequent oiling of the wood either by application of oils or from handling would no doubt make it dirty, grimy but I don't think that wood would grey as if it were left to the elements. Usually by the time it starts to grey, it has become too brittle and no longer useful as a weapon or tool.
In my opinion, I'd keep it the reddish brown and maybe make "blonde" streaks or wear patterns where the hands would cause any finishes (applied or natural) to be worn off.
Mike