May one make a Sukkah on a tree or animal?[1]
A Sukkah that is made on a tree or animal is valid, although one may not dwell in it on Shabbos or Yom Tov.[2] It is forbidden to enter the Sukkah on Shabbos or Yom Tov whether one builds the actual Sukkah, with its floor and walls, on top of the tree and rests the Sechach on top of the Sukkah walls, or build the Sukkah on the ground and simply uses the branches of the tree which are still attached to the tree to help support the Sechach.[3] Nonetheless, in the latter case, in today’s times one may be lenient to permit entering into it even on Shabbos and Yom Tov.[4] However, initially, one may not use the branches of the tree which are still attached to the tree, to support the Sechach.[5]
[1] Admur 628:5; Michaber 628:3; Mishneh Sukkah 22b
[2] Regarding if the Sukkah floor partially rests on the ground, and partially on a tree: See Admur 628:9; Michaber 628:3; Mishneh Sukkah 23a
[3] Admur 628:6 that the Shabbos prohibition applies even if only the Sechach rests on the branches
[4] Admur 628:7
[5] Admur 628:7; M”A 629:9
The reason: As initially we only use material that is Kosher for Sechach as a support for the Sechach, as explained in 629, see there for the reason. [Admur ibid]