Our grandmothers wore what they called "housecoats" way back in the day. In fact, it was fairly common among women of the era.
They were economical and cool, and ladies would wear them around the house on days when they did not intend to leave. They were for housecleaning and kitchen.
While a woman wouldn't be ashamed to invite a drop-in neighbor in for coffee, she would NEVER leave the house in her housecoat, even to go to the grocery.
Anyway, Hillary is wearing a glorified housecoat.