How do Catholics and Eastern Orthodox justify their clergy praying with those big hats on their heads?

How do Catholics and Eastern Orthodox justify their clergy praying with those big hats on their heads in the face of this scripture? > 1 Cor 11:3-4 But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. Every man praying or prophesying, having his head covered, dishonoureth his head. The head of man is Christ, and every man who prays with his head covered dishonors his head (Christ). So how can wearing big hats while praying be justified?