1 Corinthians 11: Hats?

The second half of the chapter seems easy enough to understand.  In verse 17, Paul writes that the meetings of the Corinthians 'do more harm than good'.  Tough criticism, to be sure, but Paul is clear that in their gatherings the Corinthians have divisions among them.  This is certainly not God's design for the church, as we are called to celebrate together, apparently particularly as it relates to celebrating the Lord's Supper.  And no doubt this is a serious charge, as Paul states that many in the Corinthian church have gotten sick and even died because they have taken the Lord's Supper in an unworthy, selfish manner.  'When you gather to eat, you should all eat together' (v. 33) seems to be the main point Paul makes.

The first half of the chapter is a little more difficult to figure.  Paul seems to be saying that at worship gatherings, women need to cover their heads and men must not do so.  Is this a cultural issue from long ago?  Are these clear commands to be followed even today?  Is it wrong for a man to pray while wearing a hat?  I needed to know more, so I did a little digging.  There's no shortage of explanations and guesses about the whole issue of hats, but probably the best I found comes from a sermon by Rick Stacy, as he writes about the symbolism of the head covering in those times, and how covering one's head indicated they were under the authority of another.  Rick writes:

What do we do about haircuts and hats?
For us, the answer may not be quite as obvious because our culture has changed. The principle has not changed and never will. 
Are we rebellious and arrogantly holding on to power and control. Do we demand our place of honor? Do we simply serve those in our lives?
Remember that what you do with your head often reveals what is in it.
Men, when you pray and prophesy, bow your heads –take off your caps. Let God and man know that you are under his covering and no one else’s. Don’t bring shame to your head.
Women, when you pray and prophesy, dress in a way that reserves your body for your husband. Don’t bring shame to your head.
When you pray and prophesy make sure you are under the authority of Christ, the chief shepherd and those he has given over the shepherding of the body to in his absence – the shepherds of the body.