So, "barefaced" is not wearing a mask or makeup or both?
Note that the M-W entry you linked doesn't even mention the "without makeup" definition. Neither does Dictionary.com. Or the Oxford Learner's Dictionary. Or the Macmillan dictionary.
That only the Cambridge (not Oxford) entry lists the "without makeup" definition (and lists it second / last) should be taken as a sign that that usage is rare or niche. I can in fact imagine a couple of niches where such usage might be known, but if your objective is to communicate effectively to a general audience, then you should use "barefaced" only in the sense of
- not wearing any kind of face-covering garment, such as a mask or veil, or
- open / unconcealed or exhibiting a lack of shame or scruples. [The second definition in the M-W entry you linked].
If you use it to mean "without makeup" then some people may understand you from context, but most will find your word choice odd. The normal word choice is, in fact, "without makeup" or "without any makeup".
Are "bare face" and "naked face" the same?
"Bare" and "naked" are related, but not the same or interchangeable. Idiomatic usages of these have little overlap. Any native speaker choosing "naked face" does so with the intention of drawing attention via that unusual word choice, but they probably mean the same as "bare face" -- that is, a face that is not covered by a mask, veil, etc..
Furthermore, note well that although "with her bare face" is not inherently incorrect, what you actually want in that sentence is probably "with her face bare" or "barefaced" (and we're still talking about clothes, here). The difference is subtle, but the first primes me to expect "prettier" to be a comparison with a different "she", whereas with the others I understand it to be a comparison with a different state of the same face. I'm not prepared to generalize that.
Which woman is barefaced?
Definitely not either of those wearing a mask. Perhaps there are people who would say none of them, but most would say that the one with makeup but no mask is barefaced, in the physical sense.