When creating a wash for anything, must it also be a darker version of the base colour?
WHat should I use to wash a character's face then?

I tend to use black, payne's gray or van dyke brown for most washes. For skin tones, I use a combination of burnt sienna and white and do most shadows withthinned burnt sienna, since this keeps the same warmth. For really dark sahdows, I'll use a bit of van dyke. Since this has a distinctly cooler tone, I use it very sparingly.

Al's nailed it. No need to say anything more.