Does a Sukkah require a Mezuzah?
A Sukkah is not obligated to have a Mezuzah.
A Sukkah built in a house with a removeable roof: If one’s home contains a room with a retractable roof which is turned into a Sukkah, then based on the above some Poskim learn that the room is exempt from Mezuzah throughout the duration of Sukkos. Accordingly, some Poskim rule that after Sukkos when the roof is replaced one would be required to replace the Mezuzah with a blessing, as otherwise it would be considered Taaseh Velo Min Hasuiy. Other Poskim, however, argue that in truth the removing of the roof does not make the room exempt from Mezuzah, and even if it did one would not be required to replace the Mezuzah after Sukkos being that to begin with it was placed on correctly. Practically, the custom of the world is not to replace the Mezuzah after Sukkos. However, one who desires to be stringent like the first opijnion should remove the Mezuzah after Sukkos and replace it without a blessing.
Room leading into a Sukkah: The door of a room leading into a Sukkah, such as if the Sukkah is inside one’s home on the porch, is obligated in Mezuzah even during Sukkos, as it leads into a home. However, some Poskim rule that on Erev Sukkos the Mezuzah is to be replaced to the right side going into the home throughout the duration of Sukkos, as opposed to on the right side going into the porch. However, according to the second opinion mentioned above, this is not necessary, and so is the custom to not change the position of the Mezuzah.
Sukkah leads to house: A courtyard or backyard entrance that is used as part of a Sukkah remains obligated in Mezuzah throughout Sukkos being that it leads into the home. Nonetheless, if a Sukkah is built in front of the entrance door to the home, the Sukkah is exempt from Mezuzah even though it leads into the home.
 Michaber Y.D. 286:11; See Piskeiy Teshuvos 626:11-12
 The reason: As it is not a place of permanent dwelling. [Shach 286:21; Taz 286:10]
 M”B 626:21 in implication of P”M end of 643; Shaareiy Teshuvah 626:7 in name of Peri Chadash inm Teshuvah; Bikureiy Yaakov 625:4; Kesav Sofer Y.D. 139; Shoel Umeishiv Gimel 2:166; Kaf Hachaim 626:45
 Shaareiy Teshuvah ibid in name of Peri Chadash in Tesuhvah
 Shaareiy Teshuvah ibid in name of Turei Even 14; Mateh Efraim 625:27; Derech Hachaim; Mikdash Me’at Mezuzah 286:37; Kitzur SHU”A 134:10; Aruch Hashulchan Y.D. 286:27; Maharshag 2:75
 Maharshag ibid that even Rabbanom are not Machmir in this; Kitzur SHU”A ibid; Shevet Halevi 2:153; Piskeiy Teshuvos ibid; See Misgeres Hashulchan 134:10 and Piskeiy Teshuvos ibid regarding if the Mezuzah was erected during Sukkos
 Shaareiy Teshuvah ibid
 M”B 626:21
 Bikureiy Yaakov 625:4
 Shevet Halevi ibid; Piskeiy Teshuvos ibid
 M”B 626:21
 Mikdash Me’at Mezuzah 286:37; Salmas Chaim 242; Sefer Hasukkah Hashaleim Pesakim of Rav SZ”A 14