My question, which I could have said, "Yes I know the answer to that" has just made me stop and think. I was talking with a younger man after worship services this morning and we were talking about this: "Are men permitted, scripturally, to wear a covering (hat, etc.) during worship services?" Thank you for your taking this question.
This is the other side of the issue of whether a woman should wear a head covering when praying. The passage of concern is: "Every man praying or prophesying, having his head covered, dishonors his head" (I Corinthians 11:4). Since the head of man is Christ, a man praying with his head covered is dishonoring Christ. The reason for this rule according to Paul is, "For a man indeed ought not to cover his head, since he is the image and glory of God" (I Corinthians 11:7).
Of course, whether a woman should cover her head during prayer is a contested issue among the brethren. However, consistency would demand that if one understands that God requires a head covering for the woman, then it would be required for a man to not to have a head covering. If a person is of the understanding that it doesn't matter if a woman is wearing a covering during prayer, then it would not matter if a man is or is not wearing a hat during prayer.
If a person thinks it doesn't matter, there should also be some consideration of the social customs of society. In the United States, it has long been a practice for men to remove their hats to show honor. That is why hats are removed when entering a house or when the national anthem is sung. If a person follows the custom for showing honor in some situations, but not in a religious situation, what message is being given to others?