Kay

“Rather than re-affirming his previous argument Paul draws back to nature (physis) to conclude that nature even teaches that a woman is given long hair for her glory- hence why she should not have short hair as it is a disgrace. Parallel to this is the reverse for men. Long hair was seemingly a disgrace for men and dishonouring to God when a man prayed with long hair i.e. covering.”…A woman’s long hair (femininity) and a man’s non-long hair point to both femaleness and maleness, as well as a husband and a wife.”
Mark,
Or they could be pointing to something completely different. It is also worthy of note that Greek women seem to have cut off their hair in times of mourning. Plutarch, in the context of discussing mourning at funerals, says, “So in Greece, whenever any misfortune comes, the women cut off their hair and the men let it grow . . .” (Moralia, The Roman Questions 14). This would be similar to the Jewish custom of shaving the head as a symbol of grief or mourning (cf. Deut. 21:12-13; Is. 7:20; 15:2; 22:12; Jer. 16:6; Mic. 1:16; and Josephus Antiquities iv.8.23 ).
“etiquette as regards the veil becomes stricter the more one moves east. This rule is brought out clearly by the provisions of an old Assyrian code. Married women and widows must be veiled when in public places. On the other hand, the head of the harlot, here equated with the slave, must remain unveiled under threat of severe penalties. When a man wishes to make one of these his legitimate wife, a special act of veiling is demanded. (Kittel 1965, 3:562-563)
All this applies to the city dwellers in the east, since the desert nomads seem not to have veiled their women (Hurley 1973, 194, citing Burckhardt 1830, 233-234).

The significance of this difference of customs regarding women’s headdress in the ancient world is that it shows that there was no uniform practice, especially in Greece where women often appear without a head covering in religious rites. The evidence seems to indicate that in the first century among the Romans, both men and women covered their heads at worship, while among the Greeks, both men and women uncovered their heads when they worshiped.