FLOTUS does not put her arms in her coat sleeves. She's not alone in this; other fashion-conscious women do the same. There's a name for it: shoulder-robing. But like almost everything else about her, in her shoulder-robing Melania Trump is both typical and atypical. Draping a coat over one's shoulders is practical if one wants to make a certain statement. Heavier coats tend to be more stylish, more conspicuously expensive, than light coats or sweaters. When it's too warm for a heavy coat, it's possible to show off an expensive coat by keeping the arms free so they can breathe. Impression made, problem solved.
FLOTUS has responsibilities, however, as the wife of POTUS. All her actions are political, including speech. For her, shoulder-robing is a means of hoarding her language, of saying one thing and nothing more:
When Trump leaves her arms out of her sleeves, she’s telling us she doesn’t have to perform any of the daily manual tasks the rest of us do: She will never reach for anything in a cabinet, stoop to pick anything off the ground, hold open any doors, pour any glasses of water, lift her arms to fix her hair, or fish a credit card out of a purse. If she did, her coat would slip right off.
Melania Trump does not speak, she wears. Sometime she gestures, but as little as possible.