Since the Law has not been abolished, neither has head covering, aka the tzniut that wives must wear, which is a symbol she is married, hence why Paul says, "it is a symbol of authority over her head".
The uncovering and covering cerimonail law I believe is all about the unseen reflected glory of God who remains without form
As a ceremonial law like the Sabbaths it serves as a shadow to point ahead .
Col 2:16 Let no man therefore
judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of
the sabbath days: Which
are “a shadow” of things to come; but the body
is of Christ.Col 2:17
It is not something we can judge one another in respect to but ignoring the head covering for woman,which includes the uncovering for men as ordinance of God does no go without questioning why? In that way when he comes will he find the working of His faith?
It is the first part of the break breaking ceremonial when more than one family offers worship and not the whole ordinance designed to reflect the unseen glory of God as a witness to the angels, messengers of God.
Its not a sign that a person is married but points ahead to the marriage super of the Lamb, to consummate the wedding union, the receiving of our new promised incorruptible bodies. Single woman as the bride of Christ are required just as the married here on earth. It affects single men in the same way.
For when a woman becomes married, she comes under the authority of a husband, due to the curse against Eve when she transgressed, "your desire will be for your husband, and he will rule over you". As such, when Rebekah first saw Isaac, who she was going to marry, she "veiled" herself, which is the tzniut.
Again it is in respect to both the man (no covering) and to the woman, (cover her reflective glory her hair) . She is not left without a representative glory . When gathering together the only glory that should be seen
by faith, is the unseen glory in respect to man and woman. both together representing one bride, the church