Ideally, I see nothing wrong with a woman, whenever she ought to pray, covering her head with a head covering. It was popular in Ireland before the Council, along with some other Eastern European Catholic countries.

1 Corinthians 11 is speaking about the need for women to wear veils out of submission to their husband/father (whoever is their superior). Here is the passage before verse four:

[3] 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. [4] Every man praying or prophesying with his head covered, disgraceth his head.

Also, 1 Corinthians 11:7-10:

[7] The man indeed ought not to cover his head, because he is the image and glory of God; but the woman is the glory of the man. [8] For the man is not of the woman, but the woman of the man. [9] For the man was not created for the woman, but the woman for the man. [10] Therefore ought the woman to have a power over her head, because of the angels.

1 Corinthians 11 is stressing the importance of females veiling as a sign of submission to their head. St. Paul purposefully uses the term "head" while describing the male-female relationship because the "head" refers to both the real human head and the head of the created hierarchy. Covering the female head is the recognition of their place before men, as being constructed of man rather than being built in the image of God. Bishops, Priests, and Monks visibly submit to God with their dress (cassocks, habits, etc.) and do not cover their head in submission to other men (the opposite of why women are commanded to cover their head, and why men aren't commanded to cover their head). Clerics and lay brothers cover their head solely out of reverence and adoration for Our Lord (women can do this too, but it's more precise to say they veil out of submission).

For sure, there's nothing wrong with a woman wearing head coverings, if they wish, outside of Mass. :)

I think, to the degree it doesn't resemble Muslim women, it is attractive.

Markus, here is a little quiz for you. I have seen some extremely attractive Muslim women. See if you can pick the religion of these fourteen images of
Women of various religions. I scored 10 out of 14. See how many you can get.
http://www.judaism-islam.com/quiz-can-you-tell-her-religion-from-her-head-covering/

Ideally, I see nothing wrong with a woman, whenever she ought to pray, covering her head with a head covering. It was popular in Ireland before the Council, along with some other Eastern European Catholic countries.

1 Corinthians 11 is speaking about the need for women to wear veils out of submission to their husband/father (whoever is their superior). Here is the passage before verse four:

Also, 1 Corinthians 11:7-10:

1 Corinthians 11 is stressing the importance of females veiling as a sign of submission to their head. St. Paul purposefully uses the term "head" while describing the male-female relationship because the "head" refers to both the real human head and the head of the created hierarchy. Covering the female head is the recognition of their place before men, as being constructed of man rather than being built in the image of God. Bishops, Priests, and Monks visibly submit to God with their dress (cassocks, habits, etc.) and do not cover their head in submission to other men (the opposite of why women are commanded to cover their head, and why men aren't commanded to cover their head). Clerics and lay brothers cover their head solely out of reverence and adoration for Our Lord (women can do this too, but it's more precise to say they veil out of submission).

So should men always remove hats or hoods or other things on their heads when they pray? Or only in a church building? 

So should men always remove hats or hoods or other things on their heads when they pray? Or only in a church building?

I'd say it depends on the circuмstances and if wearing the hat is required. For example, some men in the military may have to wear a hat (in my country, a beret) while in uniform. If they wish to attend Mass in uniform or need to go to confession before training and they have no time to change, it becomes a necessity and can't be circuмvented.

I have known many military traditional Catholics. They always have taken their hats off when entering a church but replaced them as soon as leaving the church.  

In some countries (such as mine), it violates the dress code if a soldier were to remove his beret. What I know is that in the US enlisted men can wear a "patrol cap" while in uniform, and not be in violation if they were to take it off. However, in my country, it's a requirement the Army doesn't overlook or excuse based on religion.  

I'd say it depends on the circuмstances and if wearing the hat is required. For example, some men in the military may have to wear a hat (in my country, a beret) while in uniform. If they wish to attend Mass in uniform or need to go to confession before training and they have no time to change, it becomes a necessity and can't be circuмvented.

I believe there is an exception for men in the military.
Dad told the story about how when he was in the Coast Guard Academy a friend who was also Catholic invited him home for dinner. It was a Friday. His friend told his mother that they had a dispensation from the rules of fast and abstinence so they could eat meat on Friday. His friend's mother replied, "Not in my house."  

13/14.  But I live in NY and have regular exposure to people from literally all over the world.  I confused the Sihk for Hindu.  Not bad considering I'm of course Catholic.