"She is wearing a black coat today" - that is fine. or "She is dressed in a black coat today" - a little awkward sounding "Today, she is dressed in a black coat" - better, but rather formal sounding. or "She has a black coat on" - this would be a good, very informal, way to say it.

No, you would not say "she is dressing a black coat today". You would need to say " she is dressed in a black coat today," as Tom suggested, to make it correct. "She is wearing a black coat today." would be perfectly acceptable.

I think that "She is wearing a black coat today" or "Today, she is wearing a black coat". Did i understand correctly your question and did i correctly answer your question? Thank's!