I talked about this in CC a little, I believe.
My angels can wear what they want with two exceptions, on duty it's always no shoes, their hair has to be long and if possible worn open. Ayil is known as a stickler for proper protocol, whereby Ariel seems to be more generous in its interpretation. Why long open hair? That's simply because I think it's hot.
Why bare feet? As angels on duty, nothing can hurt them, but they can feel. I thought it as a symbol for their connection to Earth and her creatures.