While there is a Halachic disagreement amongst Jewish scholars regarding this law, all seem to agree that it is preferable and highly praiseworthy for a woman to cover her hair even in the privacy of her own home. 

The Askmoses Answer: 

In the Talmud¹   there is a famous story about a certain woman by the name of Kimchit who was careful that “the walls of her house should not see the hairs of her head.” She was rewarded with seven sons who served as High Priests.

We see from this story that a woman’s covering her hair in private is highly praiseworthy. But is it a Torah mandate? Or is it simply a chumrah, a stringency? Must a woman cover her hair at home? King David says,²   “kol kevudah bat melech p'nimah.” All the glory of the King’s daughter is internal.

One of the expressions of this inner glory is that, in general, married women must cover their hair. But is there a halachic difference between going out in public and being at home? In the privacy of their own homes, seemingly, they should be able to “let their hair down.”

By covering her hair (even with a wig, which may be mistaken for real hair) a woman is expressing her exclusive devotion, love for, and unique connection to her husband

Once a woman is married, she enters into a completely unique relationship with her husband. This transformation is alluded to by the Hebrew name for the wedding ceremony, “Kiddushin,” which means sanctification or holiness.

Through this act, the bride and groom are totally and utterly dedicated to each other in a holy coupling. This dedication manifests itself in both an internal and an external form, in many ways, and for both partners.

One of these ways is by a woman covering her hair, which is viewed by Judaism as a sensual and private part of a married woman’s appearance. By covering her hair (even with a wig, which may be mistaken for real hair) a woman is expressing her exclusive devotion, love for, and unique connection to her husband.

Even if others do not realize that she is covering her hair, she has the constant awareness and consciousness that she is one half of a unique and profound relationship, sanctified by G-d Himself.

Now, normally, the laws of modesty are not loosened in the privacy of home. The Code of Jewish Law,³   acknowledging human nature, states that it is natural for people to act differently when they are in the privacy of their own home then when they are around a group of people.

Why? Because G-d is omnipresent; and we are always under His scrutiny. (And in case a person does not have the constant awareness of G-d’s presence, the Shulchan Aruch prescribes meditation, in order to arouse feelings of love and awe!)

However, the hair of a married woman does not have the same status as other private parts of the body that are usually covered.⁴   As explained earlier, hair covering is primarily a symbol of marriage, a demonstration of her devotion to her spouse.

So, all that said: May a women uncover her hair in private? Halachah, Jewish law, addresses public, semipublic, and private settings:

Public: The Torah states that a woman must completely cover her hair in a public place. Some opinions state that under a tefach (a handbreadth, about three inches total) of hair may show.

Semipublic: In a semipublic place, one opinion states that even if men are not usually found there, a married woman must cover her hair.

When a woman covers her hair, this brings much blessing into the home

Rabbi Moshe Feinstein disagrees with this ruling and writes that “[covering hair when in private] is praiseworthy, but not required.”

In closing, it is worth noting that the Lubavitcher Rebbe said many times that when a woman covers her hair, this brings much blessing into the home, as evidenced from these two excerpts from letters written by the Rebbe regarding hair covering:

“Moreover, from the great reward received for [covering hair] one can comprehend that there is great import to fulfilling this law.... As the Zohar states...: ‘[The woman who is scrupulous about this Mitzvah,] her children will enjoy increased stature over other children; moreover, her husband shall be blessed with all blessings, blessings of above and blessings of below, with wealth, with children and grandchildren, etc.’

“I would also add to the above, that it boggles the mind that this should be a ‘problem’ for anyone who has a spark of faith in their heart and desires that their married life be truly fortunate and blessed with these blessings and good fortune extending to the husband, wife and the children that G-d will bless them with.”⁵