Hi Colleen,
Although I am quite new to the world of painting on cookies, I may have some solutions for you. Through my own trial and error, I have discovered that painting with gel food colors has it's own unique properties. It's translucent, it dries quickly, and is difficult to layer color. That being said, it also creates a beautiful result once you have a idea how to work around those difficulties! I have found that this medium resembles watercolor and porcelain painting, and requires you to consider your light areas ahead of time. Leaving the white / light areas blank and painting around them is one solution. The other is to use an opaque color (white), The latter is not fool proof and will pick up color beneath it. I have used Wilton's White-White Icing Color. (I haven't ventured our to use a variety of products yet). Possibly another remedy to the problem with adding a mouth to the already painted beard would be to apply/pipe/paint a bit of royal icing, which is opaque, and then add some color to that after it dries. In my Silent Night cookies, I also had a dark sky painted and added stars. I used the white opaque icing color and mixed a slight bit of yellow. I added white over that to brighten. Remember if you "overwork" an area that you have painted to add another layer, it will pick up that under painting, so less is best or it will "muddy" your painting. I also use Vodka to dilute my paint as it dries faster, and I wait for the first layer of paint to dry completely before adding more.
Hopefully, this is beneficial. Remember I am new to this and there may be better solutions than what I offer. 
I am looking forward to seeing your beautiful painted cookies!
Jenny