My grandmothers wore those housecoats!
I was thinking the EXACT same thing. When my country grandmother wouldn't be leaving the house, she'd wear "housecoats" that looked JUST like what Hillary is wearing in that.
I think among ladies of that generation, they were viewed as suitable for "at home" comfort and work wear... a "clean the house" ensemble. She wouldn't be ashamed to entertain a drop-in neighbor, but she wouldn't go to town, even to shop for groceries, in it either.