My dad said his mother used to do her housework with her hat on because she never knew when she would have to go out to deal with one of her sons getting in trouble down on the wharf or somewhere -- but I think he was exaggerating ;) Of course, she never wore trousers and neither did my other grandmother, even though she was quite a bit younger and more modern than Granny.
Granny used to come to town twice a year - once in the spring to get a new hat for summer and once in the fall to get a new winter hat. I have a picture of her pushing Dad in his pram ( 1920 - ish) and she is wearing this gorgeous big-brimmed hat.