Among the reformed churches that do not mandate hat wearing there are a few different reasons as to why we do not. The first view is what may be called "the cultural view". This view is exemplified by pastor/theologian John MacArthur in his commentary on First Corinthians where he states "It seems, therefore, that Paul is not stating a divine universal requirement but simply acknowledging a local custom". While I can respect John's having a reason for not demanding headwear, I do not agree with his reason. As Charles Ryrie states in the note in his study Bible, advocating women should wear hats,"Paul's reasons were based on theology(headship, v. 3), the order in creation (vv. 7-9), and the presence of angels in the meeting (v. 10)" and not in defence of a social custom. Paul elsewhere (eg. Rom. 14)clearly allows for differences in the church over social customs and yet here he commands head covering for women and none for men. So the answer must be sought in a more appropriate understanding.
This appropriate understanding is the second view which may be called simply "the hair view". In this view the covering Paul was speaking of is "hair" and not a hat, veil, doily or any other man-made material. This view sees it unlikely that Paul would be making a new law for women never before established in scripture. We are not told God created a hat for Eve in the garden so as to worship him appropriately. The Old Testament laws were very thorough in their mandates for worship and again they are silent on this issue. The best evidence comes from the text itself when Paul states in verses 14 and 15 "Does not even nature itself teach you that if a man has long hair, it is a dishonor to him, but if a woman has long hair, it is a glory to her? For her hair is given to her for a covering." Notice Paul appeals to common sense here. Although it is now codified in his writing it, Paul was asking what was evident in nature and not written in scripture until then. I make this point in passing to point out that while I hold tenaciously to the reformation principle of sola scriptura(see my blog "Holy Bible" January 2007), we should not neglect what God has taught us in nature through common sense. So Paul has defined his meaning with these verses. Nature does not teach us anything about hats, veils or doilies or which is more appropriate. Paul's point to the church at Corinth is that it is wrong for men to have long hair and women to have short hair. God hates confusion and it is against the natural order for men to have long hair and women short. Even the angels get confused (v. 10)as they look on unlike the angels that fell in Genesis 6:1,2 who clearly knew who the daughters of men were. Reformed churches that teach "head coverings" that I am aware of typically use the doily which does not fully cover the head. If they want to meet this honestly they should be like the muslim women pictured above.
In conclusion, it is important to say that I do not believe it is a sin for a woman to wear a hat to church but it is not mandated by scripture. It is also important to say at this juncture that nowhere in scripture does it define long hair or short hair and so I as Paul appeal to common sense in this matter. Some may not think my wife has long hair, and compared to say Crystal Gayle she does not, but if my hair were her length it would generally be considered long. There must be some christian liberty in our judgment of this.
First Corinthians: A Contemporary Commentary by Gordon H. Clark
Exposition of the Old and New Testaments Vol. 8 John To Galatians by John Gill
The MacArthur New Testament Commentary 1 Corinthians by John MacArthur
Ryrie Study Bible Expanded Edition (NAS) study notes by Charles Ryrie