I imagine it'd have the full face on it, but could be folded in such a way that it only shows the mouth when worn in the way of a mask.
I mean, I got the idea from existing bandana designs that work in a similar way. I got a side-by-side of someone wearing a design I actually managed to find the unfolded version of (hooray for google).
I imagine a Mud smiley bandana would be a little plainer than that, mind. And I keep looking back and agreeing with you guys more and more that the OWI logo doesn't look right on that sketch I did. Definitely would be better as a plainer design.