Gemara

(Beraisa): The Azarah cried out to expel Yisachar of Kefar Barkai, who honored himself and disgraced Kodshim.

He would wrap his hands in silk during the Avodah.

Sukah 37b - Rabah (to people who prepared the Reish Galusa's Lulav bundle): Leave a place uncovered for him to hold it, lest it be a Chatzitzah.

(Rava): Anything to beautify is not a Chatzitzah.

(Rabah): One may not hold the Lulav through a cloth. We require 'Lekichah Tamah' (taking without interruption).

(Rava): Taking through [holding] something else is called taking.

(Rava): If one picked up [the Minim] through something else, he was not Yotzei.

Question: Rava holds that taking through something else is called taking!

Answer: He said so about taking it honorably, but not disgracefully.

Rishonim

Rif and Rosh (Sukah 18a and 3:24): The Halachah follows Rava in all these Halachos.

Ran (DH Lo): Since a cloth wrapped around his hand is not to beautify the Lulav, why isn't it a Chatzitzah? No verse disqualifies Chatzitzah for Lulav. The concern is for Lekichah Tamah. Whatever is to beautify it, is Batel to the Lulav. What is Tafel (secondary) to his hand is Batel to his hand. It is as if he touches the Lulav itself.

Tosfos (57a DH d'Karich): Rashi explains that if one's hands are wrapped in silk during Avodah, it is a Chatzitzah, and it is Pasul. "v'Lakach ha'Kohen" obligates taking [the Kli or Kodshim] by himself [in his hands].

Rashi (42a DH Derech): It is honorable when he wraps his hands in a cloth. Taking the Minim in a bowl is disgraceful.

Tosfos (37a DH d'Ba'ina): Chatzitzah applies when he wrapped the Lulav, but not when he wrapped his hands. Rashi says that it was a Chatzitzah for Yisachar, because he intended for his honor, lest his hands get dirty. Alternatively, the only problem was disgrace to Kodshim. I disagree. Chatzitzah applies to something needed to tie the Minim together. Rather, the cloth was a holder for the Lulav.

Poskim

Shulchan Aruch (OC 651:7): If he wrapped a cloth around the Lulav, or wrapped a cloth around his hand and took it, some say that he was not Yotzei.

Magen Avraham (16): He says 'some say...', because when he wrapped his hand, the Ran says that he was Yotzei.

Gra (DH Yesh): The Ran and Ritva hold that Chatzitzah does not apply. Anything to beautify it, or that is Batel to his hand, is Lekichah Tamah.

Mishnah Berurah (33): Likewise, if he wore gloves, he was not Yotzei.

Rema: The custom is to be stringent and remove Tefilin and rings from the hands, but letter of the law there is no concern, since the entire hand is not covered.

Beis Yosef (DH Matzasi): The Agudah says that we remove whatever separates between the hand and the Lulav, e.g. Tzitzis, Tefilin, and women remove rings. I say that one must remove them only if they cover the entire hand.

Rebuttal (Bach DH Kosav): Rava permitted the tie on the Lulav only because it is to beautify it. Anything to beautify it, if is not Mino, e.g. Tzitzis, Tefilin and rings, disqualifies, even if the Chatzitzah is only on part of the Minim.

Defense (Magen Avraham 18): The Agudah holds that when the entire hand is not covered, the covering is Batel to the hand. We do not say so about what is used to tie the Lulav.

Taz (7): Why is the Beis Yosef lenient if they do not cover the entire hand? The Ran connotes that this is like Tevilah and Tefilin! (Even a partial Chatzitzah is a problem,) Tosfos connotes that Rava agrees that what is not to beautify it is a Chatzitzah.

Gra: According to the Ran, this is not letter of the law, for they are Batel to his hand. According to Tosfos, it is a Chatzitzah, and we do not distinguish [between part or all of the hand]. Even one hair is a Chatzitzah for Bigdei Kehunah (Zevachim 19a)! A reed over a wound may not be in a place used for Avodah, and we asked whether wind or earth are Chatzitzos (ibid.)!

Chasam Sofer (YD 192 DH Emnam): The Yam Shel Shlomo (Chulin 8:21) says that a man's ring without a stone is not a Chatzitzah (for Netilas Yadayim). One does not remove rings when putting on Tefilin or taking the Lulav because he is particular about this, rather, to make room for the Tefilin or Lulav.

Mishnah Berurah (35): Some say that he folds the Tefilin (strap) in back of his finger (where he holds the Minim). Others say that he totally removes Tefilin before taking the Lulav.

Mishnah Berurah (36): Several Acharonim say that letter of the law, we are concerned for a Chatzitzah on part of the hand. Therefore, if he did not remove the Tefilin or ring, he takes the Lulav again without a Berachah.

Kaf ha'Chayim (78): Likewise, one must remove a bandage form the hand before taking the Lulav.

Shulchan Aruch (YD 271:7): One must write a Sefer Torah with his right hand.

Birkei Yosef (10, citing Maharam Provintzal 33): One may not write even crowns on the letters with gloves on, even if the ends of the fingers of the gloves are cut [and his fingers stick out], even if it is very cold, for this is not honorable for the Sefer Torah.

Pischei Teshuvah (19): Also Ma'aseh Roke'ach (on Rambam Hilchos Sefer Torah 2:8) brings so from Maharam Provintzal. The episode with Yisachar alludes to the law, but it is not a proof. There, he wrapped his hands in silk and profaned Kodshim. Rashi says that a Chatzitzah disqualifies. Also, it was disgraceful.

Ha'arah 4 (on Birkei Yosef): Pischei Teshuvah did not see the Teshuvah. Maharam Provintzal himself brought the episode with Yisachar, and forbids doing any matter of Kedushah in gloves, e.g. Bris Milah or Shechitah. This requires investigation. How can we learn about gloves for the cold from Yisachar? Chatzitzah does not apply writing a Sefer Torah and other Mitzvos. Tosfos (37a) says that the problem was that Yisachar honored himself, lest his hands get dirty. This does not apply to gloves for the cold, especially if his fingers stick through and hold the quill.

Torah Lishmah (attributed to the Ben Ish Chai, 26): People often wear gloves when it is cold. One reading from the Sefer Torah may not hold it through gloves. This is like the case of Yisachar. It is not honorable for the Sefer Torah.

Igros Moshe (YD 2:16): When checking the lungs, one must feel for lesions and any change. Surely one may not wear even the thinnest gloves. If one's skin is covered, his sense of feel is hampered. This is less severe than checking a knife. We check a knife multiple times, for sometimes one feels a nick only the second or third time, because at first he did not concentrate so well. We are more lenient about checking the lungs, for most animals are Kosher. When checking the knife, the animal has Chezkas Isur. Even so, if one knows that his mind is not settled now, presumably he may not check [even lungs]. If the entire fingers are exposed and the glove covers only the palm, he can feel properly. However, if even a minority of the fingers are covered, his fingers are less mobile, and this inhibits feeling. It is good to be stringent that even the palm is not covered.

Igros Moshe: The questioner said that according to the opinion that Shechitah is a Mitzvah, it is a disgrace to slaughter with gloves, like the case of Yisachar. It was a Chatzitzah and a disgrace to Kodshim (Rashi). In Sukah (42), Rashi permits taking a Lulav through hands wrapped in a scarf. Rava considers this honorable! Tosfos says that Yisachar was concerned for his honor, lest his hands get dirty. Perhaps Shechitah [of Chulin] is different, for blood is not part of the Mitzvah. Shechitah without blood is Kosher. Therefore, one may seek a way to avoid getting dirty from blood. It is not a disgrace to the Mitzvah of Shechitah, especially if he wears gloves due to the cold, and Chatzitzah does not apply.

Igros Moshe (DH v'Nimtza): When there is a Mitzvah to touch something that dirties his hands, one should be happy to dirty his hands with the Mitzvah and not seek ways to keep them clean. Wearing gloves shows contempt for the Mitzvah. Perhaps he would refrain if he could not keep them clean! People realize that this does not apply to Lulav, and all the more so one who wears them due to the Isur to touch a Sefer Torah with his hands. This honors the Mitzvah! However, since blood exudes in every Shechitah, perhaps it looks like he would refrain if not for the gloves. However, there is no Mitzvah to slaughter one's own meat, so it does not appear so disgraceful. One should not wear gloves without need. However, it is forbidden to wear thick gloves, lest he not feel if he pressed or paused a small amount, since it is hard to work with them.