Remember Winterfell during the first season? Sansa had handmaidens, young women who live in the castle with her. There were old women, septas (who Stannis may or may not have thrown out of Dragsonstone), there were butchers (remember Arya's friend who The Hound killed?), the families of some of the soldiers he took with him would be there. Stannis being there or not, there are people who live and work there. Them fleeing because he died doesn't make sense. Again -- Are they supposed to go live with their families in the countryside who would be poor and live rough? During winter? Doubtful.