I would cover them with wallpaper.

You can put window film on them that looks like frosted glass -or - frost them w/o the window film.

I find drapes to cover closets a cheap look I have seen them wallpapered and its okay but honestly replacing with bifold doors will allow full access and upgrade the look for sure. Since you have shutters on the windows you could use louvered doors.

If you have/will you put mirrors elsewhere in these rooms (because You need mirrors somewhere), then I would suggest replacing the doors with louvered doors as suggested above. If you need to keep these mirrors and just to update the look, you can add some sort of perimeter trim around them.

I am replacing my mirrored closet doors with mirrored closet doors in my current remodel.

I find having a full length mirror to be highly functional. It also opens up the room and brings in my view. My new mirrored doors will have different hardware so the suggestion of painting the hardware dark is the most valid suggestion.

Frankly I think curtains on a closet door look tacky and I don't understand how wallpapering them is more visually pleasing.

first cover them with any kind of paper... just plain brown paper. and then before you do anything permanent/expensive you can better decide if you never used the mirrors and that you werent accustomed to having a lot of reflected light in the bedroom. your bedroom can't help but be suddenly smaller and darker.

you do not want to pay for a 'don't it always seem to go, you don't know what you got til its gone' situation.

dusting louvered doors isnt so bad... i do it top to bottom with a dry angled 1 1/2 inch paintbrush, corners to middles, with a piece of newspaper on the floor to catch it all.