Married women covering their hair even when alone at home:
Some Poskim rule that, from the letter of the law, a married woman is not required to cover her hair in the privacy of her home or room when no one else is around. [According to this opinion, she may do so even when she is a Niddah, if her husband is not around.] Other Poskim, however, rule that it is forbidden to do so even in her own home, even when she is alone in her room. Whatever the case, the Talmud and Poskim encourage a woman to cover her hair at all times, even in the privacy of her home, and doing so merits one to have children fit to be Kohanim Gedolim. Furthermore, according to the Zohar, it is a complete prohibition to reveal even a single hair of the head, even in one’s home, and, “one who is not careful in this, causes their home to be stricken with poverty, the side of evil, and causes spiritual challenges for their children, as well as other Tzaros; while one who is careful in this merits to have illustrious children, and have her husband be blessed with all blessings of above and below, with wealth and grandchildren.” This Zoharic statement is recorded in the Poskim and they conclude that it is proper to be followed. The Rebbe on many occasions encouraged women to follow this act of piety and benefit from its positive affect on one’s children, and so is the custom of all G-d fearing women today, to not uncover their hair even in the privacy of their own home. Some Poskim rule that according to the Zohar, which prohibits to reveal any hair of the head, the sideburn areas and neck areas of her hair is also included, and it is not to be revealed even in the privacy of one’s home.
It is disputed amongst Poskim as to whether a wife must cover her hair even in the privacy of her home when no one is around. Nonetheless, based on the Talmud and Zohar, women are particular to never reveal their hair in the open, even in the privacy of their bedroom. This Talmudic and Zoharic teaching is recorded in the Poskim, and is encouraged to be followed by all. Many blessings are stated to be given to those who are careful to abide by this.
May a married woman uncover her hair in the shower?
Yes. Even according to the Zohar, it is permitted for the hair to be uncovered in the shower, as it is necessary for washing the hair. There is no need to be stringent to wear a head covering of any sort while in the shower.
 See M”B 75:14 and Biur Halacha “Michutz”; Ketzos Hashulchan 9:4 footnote 11; Sefer Kevoda Bas Melech [Weiner] 43-53; Sefer Shemiras Haguf Vihanefesh [Lerner] 255
 M”A 75:4 that so is implied from E.H. 21:2 and so writes Tosafos Kesubos 72b, brought in Biur Halacha ibid, that “Specifically in the marketplace is it forbidden, but in the courtyard where people are not found it is permitted there to walk with revealed hair.”; Igros Moshe E.H. 1:58 and Y.D. 2:35 concludes that it is not a requirement, and that even a Torah scholar may marry a girl who does not cover her hair at home; See regarding the allowance for the husband to see her hair: Nazir 28a, “I don’t desire a woman without hair”; Tzemach Tzedek E.H. 139:2 that a woman’s hair is only an Erva to others, and not to her husband, and that every woman is particular to not show her hair to any man in the world except her husband”; Igros Kodesh 15:415 that the Rebbe explains that a woman’s hair is only an Ervah, and only gives Yenika to Kelipos, when strangers see it, as opposed to her husband, “On the contrary, he can claim that he does not desire a woman with shaven hair”
 The Tznius prohibition applicable even in the privacy of one’s home: Vetzaruch Iyun why uncovering the hair in the home is not prohibited even according to the above opinion due to it transgressing the general Tznius laws which require all normally covered parts of the body to remain covered. Most puzzlingly, such an argument has not been raised even by the stringent opinions brought above as a reason for their opinion of prohibition. One cannot argue that it is permitted to do so, being that one’s actual skin is not revealed, as Admur [Basra 2:6, “Today, in our times, since it is common for everyone to always cover their heads, it is always forbidden to walk, or even sit, with one’s head uncovered, as by doing so one reveals an area of the body which is commonly covered, and it is thus immodest.”] rules that it is forbidden for a man today to even sit without a Yarmulka on due to the Tznius regulations, as today it is considered a normally covered part of the body and hence why should a woman’s hair be any different! However, in truth, one can suggest that since single girls do not cover their hair, therefore even when one gets married we cannot consider it as a normally covered part of the body which requires constant covering even in the privacy of one’s home. It is not similar to men’s head covering, of which all orthodox Jews are accustomed to wear at all times, irrelevant of age or status of marriage. Now, although children of very young age, below three years old, do not wear Yarmulkas, this is because at this age the Tznius laws do not yet apply, and thus it cannot be used as a reason to permit un-Tznius dress later on even in the privacy of one’s home.
 Some Poskim rule that it is forbidden from the letter of the law for a woman to reveal her hair even in the courtyard where people are not found. [Tur E.H. 115, Bach E.H. 115:2 in name of Rambam, Semag Asei 48 in name of Yerushalmi Kesubos 7:6, Beis Shmuel E.H. 115:9, brought in Biur Halacha ibid] Furthermore, some Poskim rule that it is forbidden to do so even in her own home, even when she is alone. [Bach ibid, Beis Shmuel ibid that it is forbidden under Das Yehudis even in her own room, brought in Biur Halacha ibid; Chasam Sofer 36 regarding Chatzer and house that so rules the Tur, Shulchan Aruch, Bach and Rambam and that the custom is to rule like this opinion; Nachalas Tzevi E.H. 21:7; Mayim Rabim E.H. 30; Biur Halacha ibid who questions proof of M”A; Kevoda Bas Melech [Weiner] pp. 44-46 in name of Bach and Beis Shmuel regarding Chatzer and that the same applies regarding a house]
 Yuma 47a regarding Kimchis, that she merited to have seven sons who were fit to be high priests due to that, “the locks of her hair never saw the walls of her home”; Yerushalmi Yuma 1:1; Megillah 1:10; Horiyos 3:2; Vayikra Raba 20:11; Tanchuma Acharei 7
 Siddur Ya’avetz Mosach Hashabbos Mitos Kesef 7 Chulya Beis 2; M”B 75:14 based on statement of Zohar and Kimchis
 Zohar Parshas Nasso p. 239, brought in M”A 75:4, “The Zohar is very stringent that no hair be seen”; Maharam Alshiker 35; Chasam Sofer ibid; M”B 75:14
 M”A 75:4, “And so is proper to follow”; M”B ibid; Chasam Sofer 36 concludes that in our lands so is required from the letter of the law, and revealing even one hair, even in privately, is an Ervah. [He writes that while the Talmudic law does not require covering in the home, the Zohar does, and since the custom of the world is like the Zohar, therefore so is the Halacha and it is forbidden to be lenient. In his words, “Since in our lands the custom is like the Zohar, it uproots the Halacha.”] Igros Moshe E.H. 1:58 and Y.D. 2:35 concludes in negation of Chasam Sofer and that it is not a requirement to follow, and that even a Torah scholar should not break a Shidduch because of this, although agrees that it is proper to follow!
 Likkutei Sichos 2:319; Hisvadyus 5742 pp. 2190-2191; Igros Kodesh 8:204
 See Chasam Sofer ibid; Teshuvah Meahavah 48; Kevoda Bas Melech [Weiner] p. 51 [although he omits the Chasam Sofer]
 Pashut, and so is implied from the ruling of Tznius that it does not apply to a bathhouse. See Admur Basra 2:2; M”A 2:2; See also Tosafos Yisheinim Yuma ibid; So also writes: Kevoda Bas Melech [Weiner] p. 52; Piskeiy Teshuvos 75 footnote 96
 The Reason: An exception to the above rule of modesty is by a bathhouse or river, as in these places it is common to walk around naked, and it’s not possible to be clothed. Thus, being unclothed in such a place does not break the code of modesty. [Admur ibid]