Praise be to Allah.
The Muslim woman is required to cover all of her body in front of men. Hence she is allowed to let her garment drag by being a cubit longer in order to cover her feet. What the woman has to do is to cover her feet either by wearing a loose and long garment or by wearing socks or the like. If she covers her feet then she does not have to wear socks, but if she wears socks this will be more covering, so it is recommended. And Allaah knows best.