TL

The idea of a woman wearing a covering on her head is a human one. It was never instigated in the Torah. Headcoverings were culturally determined and different in different cultures.

Such things are not things God is concerned with. If He had been concerned, He would have brought Eve to Adam with a proper covering over her head and body. God is concerned with morals, character, integrity, and the things of the spirit and soul. And yes, these things do affect what we wear, but in the sense of modesty and not offending other’s cultures. That’s about it.