I roll very dry, everything as dry as possible, no dampness or moisture to the touch, so I can't say. I can say that my ashes are generally very white, though.
Just from what I have read the color of ash is related to the minerality of the soil the wrapper was grown in. I've never rolled a cigar so I have no practical experience but if you have "hard' water I don't see how that wouldn't affect the color of the ash. Curious what you would find if you used distilled water while rolling.