What is the reasoning behind the Halachic opinion that widows and divorced women should continue to cover their hair?
Shalom U'Varacha The Gemara tells us that the reason that a woman has to cover her hair is as hair is considered one of the covered areas of the body. Like all the other areas of the body that need to be convered for modesty it is forbidden for a woman to leave these areas revealed and for men to see her like this. The simple explanation of the Gemara is that this includes all women both married and single but we do not hold like this. Rather the Halachah is that a married woman has to cover her hair. Once she has been included in this category even if she is no longer married the obligation to cover her hair still remains as her hair is now considered a covered area of her body. In specific cases where the woman may feel that she needs to receive special consideration she should contact a Rav. Kol Tuv