A halocho sheet given out in my shul says that there is an order to washing (e.g. on Erev Shabbos) – first face then right hand, left hand and finally feet. The source is given as מחזיק ברכה ר״ס, ג.
I had always thought that פניו ידיו ורגליו was a phrase but not a specified order because it is difficult to imagine washing the face before the hands.
Are there other sources which discuss the order of washing hands, face and feet?