But he did use the issue of hair, whether cut or uncut, long or not, to illustrate his point. He did say in the latter part of verse 5 regarding a woman praying or prophesying with her head uncovered that it "...is even all one as if she were shaven." Now the word for "uncovered" in the Greek according to Strong's Greek Dictionary is "akatakaluptos," which is derived from the term a (as in apolitical) and a combination of two other Greek words, kata and kalupto. Specifically a (as a negative particle) and a derivative of a compound of Kata and Kalupto; and has the meaning, unveiled: - uncovered. To me it interesting to note that the word for the man who shames his Head (Christ) by praying or prophesying with his head kephalē (which is derived from kapto and kata) covered does a dishonorable act. That, no doubt, is why men take their hats off when they pray or when prayer is made in their presence.
Heavy stuff? Inspired words? So the term akatakaluptos means uncovered or unveiled and the word peribolaion (used later) means in the Greek, "a mantle, veil: - covering." Paul goes on with his illustration. In verse 6, the Apostle says that if it is shame (here the Greek word is aischron which means a shameful thing) for a woman to be uncovered, she should be shorn (here the Greek is keirō which means to shear). Therefore if the woman "be not covered," when she prays or prophesies, she causes shame to her head (presumably the man). Thus the Apostle Paul instructed that "if it be a shame for a woman to be shorn or shaven, let her be covered." Presumably have a veil on her head.
In verse 7 he comes back to his original premise by saying, "...a man indeed ought not to cover his head, (again he should take off his head covering or hat) forasmuch as he is the image and glory of God: but the woman is the glory of the man." Remember Paul's beginning premise of giving glory to one's head. Thus the man should not pray or prophesy with his head covered (having a hat on) and the woman should not pray or prophesy with her head uncovered (without her head being veiled) for to do so dishonors their respective heads (that is Christ for the man and the man for the woman).
In verses 8-12, Paul declares that neither the man or the woman are complete without the other, "but all things (are) of God." (I will not try to address verse 10 regarding a woman having power on her head because of the angels, but I don't think it means that her long hair gives her special power, either for protection of the church or to bring revival. I do, however, think it refers back to Apostle Paul's original premise stated in verses 3-5.
The Holy Ghost anointed Apostle is saying that a woman's long, uncut hair is given her for a veil. Now either Paul was speaking under the anointing of the Holy Ghost or he wasn't. If he was just stating his opinion, then the ladies who cut their hair have nothing to worry about. But if he was speaking words inspired by God, well as the song says, "There's a great day coming, a great day coming there's a great day coming by and by..."