Children wearing clothing of the opposite gender:
It is a Biblical prohibition for a man to wear the clothing of a woman or a woman to wear the clothing of a man. It is disputed as to whether the prohibition of Lo Silbash only applies when one wears the opposite gender’s clothing for the purpose of resembling the opposite gender, or even if one wears it for other purposes, such as to protect one from the cold, or from the sun. Practically one may be lenient in this matter in a time of need. The following will discuss this prohibition vis a vis children:
May children dress themselves with clothing of the opposite gender?
Children who have reached the age of Chinuch must be educated not to dress in clothing of the opposite gender [unless there is no other clothing available and they need to wear it to protect from the cold or the sun]. Some write this begins from age six. Other’s write this begins from age three. Other Poskim rule the obligation to educate the child begins from the age in which the child or/and parents are embarrassed for him/her to wear clothing of the opposite gender.
May one dress children under the age of Chinuch in clothing of the opposite gender?
Some Poskim rule that children of all ages, even below Chinuch and even a baby, may not have clothing of the opposite gender placed on them [unless there is no other clothing available and they need to wear it to protect from the cold or the sun]. Other Poskim however rule one may dress children in opposite gender clothing until the child is of age that he/she, or the parents, are embarrassed for him/her to wear clothing of the opposite gender. According to Kaballah, one is to be very careful to avoid placing the clothing of a female on a male child or vice versa even by a newborn child, as explained below.
May one place a Yarmulke on a baby daughter’s head? This is subject to the same dispute as crossdressing for the sake of jest and fun, explained above, and to whether the prohibition applies to children below the age of Chinuch/embarrassment.
May children cross dress for a skit, play and the other purposes of the like?
No. However, if he/she remains recognizable as a man/woman and merely wears a single clothing of the opposite gender, there is room to be lenient. Many however are stringent in all cases, and the Rebbe expressed contempt for children who cross-dress for school plays and the like.
The severity of crossdressing a child in Kabala:
The Shlah Hakadosh relates in the name of Rav Menachem Habavli that the reason behind the prohibition to cross-dress is because a clothing effects a person’s thoughts and emotions, and if one wears clothing of the opposite gender, it causes one to have an inclination towards promiscuity. Accordingly, it is written in Sefarim that when a child exits his mother’s womb, if the child is wrapped in a garment that is not of his gender, such as a male child in a female garment, or a female child in a male garment, then that child will have a very promiscuous inclination. Therefore, [since the gender of the child is unknown] one must be careful to wrap the child in a new garment.
 Yoreh Deah 182:5; Rambam Avodas Kochavim 12:10; Nazir 59a; Parshas Ki Seitzei “Lo Yihyeh Keli Gever..” “Lo Yilbash Gever Simlas Isha”; Taz 182:6; Chinuch Mitzvas 542 [women crossdressing] 543 [Men crossdressing]; Rambam Sefer Hamitzvos Mitzvah 40; In Hilchos Avodas Kochavim it is listed as two Mitzvos;
 The Poskim who permit: Shach 182:7 in name of Bach; Taz 182:4; Avnei Tzedek 72; Shraga Hameir 7:124 that the Shach agrees with the Bach on this matter; See Darkei Teshuvah 182:9; See also Admur 301:6 based on M”A 301:16 and Gemara Shabbos that a female ring is not considered a Shinuiy for a a man to carry through wearing on his finger on Shabbos being that at times during the week they wear it on their finger to bring it to be fixed. Thus we see that if one wears the item for non-cross-dressing purposes, it is permitted
The Poskim who prohibit: Yad Haketana 2:6 [p. 279], brought in Darkei Teshuvah 182:9; Binas Adam 90:94; The Shach ibid questions the ruling of the Bach, although some write that his question is not relating to this matter, of which he also agrees; See Divrei Chaim 2:62 [prohibits even to prevent pain]; Maharsham 2:243; Yabia Omer 6:14-4
 Shraga Hameir 7:124; Maharsham 2:243 rules one may only be lenient if it is recognizable to the viewer that one is doing so due to the cole and the like; Bach ibid writes one may be lenient because one has no other choice; See Minchas Yitzchak 2:108-4
 Meaning that they are getting dressed themselves, regarding if they may be dressed by an adult-see next Q&A!
 Admur 343:2-3 regarding all Mitzvos; Shevet Halevi 6:118-4
 See Ohel Yaakov p. 291
 See Ohel Yaakov ibid footnote 33 in name of Rav Elyashiv
 Igros Moshe E.H. 4:62-4
 Minchas Yitzchak 2:108; Kerem Shlomo 17-3; Minchas Peri 2:66; Poskim brought in Ohel Yaakov 292
 See Minchas Yitzchak ibid
The reason: As it is forbidden for an adult to dress even a child with men’s clothing as it is forbidden to feed a prohibition to a child of any age. [Minchas Yitzchak ibid, based on Admur 343:2]
 Igros Moshe E.H. 4:62-4
 Shlah Hakadosh Parshas Ki Seitzei in name of Rav Menachem Habavli Taamei Hamitzvos Lavin 313-314
 Shevet Hakehasi 2:258; Mishneh Halachos 7:43; Ohel Yaakov p. 288
The reason: This matter is subject to the same dispute mentioned regarding cross-dressing on Purim or for a wedding, in which we concluded like the stringent opinion. Furthermore, there is room to learn that in this case it would be forbidden according to all, being that the joy of Purim and a wedding is Simcha related, as opposed to a mere skit. [Shevet Hakehasi ibid]
 As the implication from the Poskim is that whenever the dressing is done for jest and not for promiscuity, it is permitted if one’s gender remains recognizable, even if the joy is not for the sake of a Mitzvah.
 Ohel Yaakov p. 287 in name of Harav Gerelitz that it is forbidden for girls in a play to wear a hat or Tzitzis; Orchos Rabbeinu 1:226
 Igros Kodesh 10:238, printed in Shulchan Menachem 5:56
 Parshas Ki Seitzei
 Taamei Hamitzvos Lavin 313-314
 It is unclear if the intent here is a garment that is made for a female versus male, or a garment worn by a female versus male, or both.