I've never heard the word Mien before until today, and I am wondering how it might differ from the word Countenance.
From the OED:
A person's appearance or manner, especially as an indication of their character or mood.
‘he has a cautious, academic mien’
A person's face or facial expression.
‘his impenetrable eyes and inscrutable countenance give little away’
While it seems that countenance is simply their facial expression, I can't think of a situation where a person has a facial expression for any other reason than indicating how they are feeling, since it is indeed an expression. Therefore it gives it to me the implied same definition of being an indication of their character or mood.
So I am left thinking the only difference could be appearance/manner vs. facial expression. So you could perhaps say:
His hat was tilted to obscure his face, giving him a distrustful mien.
But I sorta feel like you could use countenance for non-face related expressions, it feels like a countenance is a kind of 'read' you get on a person.
If you're outright, then I can feel it might not make sense, like this:
The scars and tattoos on his arms gave him an evil countenance.
Which I am not 100% sure is incorrect but it feels like it's heading that way.
His grin, along with the scars and tattoos on his arms gave him an evil countenance.
Yes, his grin works but the rest of the sentence isn't connected to countenance. It feels like it'd be the same as saying 'His raspy voice and scars and tattoos made him sound evil', like the scars and tattoos don't have an effect on the descriptive noun.
I am a bit puzzled. I also wonder if Mien is actually a word in common-usage. It isn't suggested as archaic but I have never heard of it before today.
Likewise with Mien, could you use it without an indication of their character or mood? It says especially, but it feels odd to say
The long yellow scarf and pink high boots gave him a colourful mien.
His mien was plain, he was of average height, weight, and was very unremarkable.