For after this manner in the old time the holy women also, who trusted in God, adorned themselves, being in subjection unto their own husbands:
In [1 Peter 3:4,5], God speaks of our covering/adornment as a picture of our character/behavior. I believe that the clothing mentioned in Deuteronomy represents the character we put on. A woman is not to desire to be a man & a man is not to desire or seek after being a woman. I believe it is about where our hearts are in regards to the gender God perfectly created us to be.