Tirmidhi

Commentary:
(1)
Wiping (masah) of the head can be performed directly on the head, or over a turban (imamah) or a cloth tied on the head such as a scarf (dupatta), and it is also permissible to begin wiping on the head and complete it on the turban.
There is no clear evidence for wiping only a quarter of the head.

(2)
In this hadith, "khimar" refers to a turban or any cloth tied on the head, such as a headband, etc.

(3)
Wiping over the turban (imamah) is narrated from a group of the noble Companions (radi Allahu anhum). Thus, Imam Tirmidhi rahimahullah writes: This is the opinion of a group of the Companions (radi Allahu anhum), among whom are Abu Bakr, Umar, and Anas (radi Allahu anhum), and it is also narrated regarding this from Abu Umamah, Sa'd bin Malik, and Abu Darda (radi Allahu anhum).

(4)
According to most scholars, it is not a condition for wiping over the turban (imamah) that it be tied after performing ablution (wudu).

104. Commentary:

➊ By «الْخِمَار» is meant something that covers the head; here, it refers to a turban or an 'imamah. It does not refer to a general head covering.

➋ Wiping (masah) over only the turban is a matter of scholarly disagreement. The apparent wording of this hadith indicates that it is permissible to wipe over only the turban as well. There is no reason to deny this. As for the Hanafi position that the narration about wiping over the turban should be interpreted in light of the narration about wiping over both the forehead and the turban, this reconciliation would only be possible if the narrator of the incident were the same Companion. However, even in that case, the correct opinion is that it is not far-fetched that the Companion observed two different situations and then narrated them accordingly—sometimes in one way and sometimes in another, as is narrated regarding the eclipse of the sun and other matters. Here, however, the Companions who mention both types of wiping are different, which indicates that both methods are established from the Prophet sallallahu alayhi wa sallam, and the Companions observed both methods. Therefore, just as it is permissible to wipe over the turban along with the forehead in light of the narration of Mughirah ibn Shu'bah, it is also permissible to wipe over only the turban based on the hadith narrated from Bilal radi Allahu anhu. And Allah knows best. For further details, see: [محلی ابن حزم : 58/2]

Benefit:
It is established from this that wiping (masah) over leather socks (khuffayn) and the turban (‘imamah) is permissible. Wiping over the turban is a Sunnah. A few evidences are presented below.

Evidence No. ➊ ... «عـن عـمرو بن أميه قال : رأيت النبى صلى الله عليه وسلم يـمسـح على عمامته و خفيه» ... Sayyiduna ‘Amr bin Umayyah Damri radi Allahu anhu narrates: I saw the Prophet sallallahu alayhi wa sallam. He wiped over his turban and both leather socks. (Sahih Bukhari, Hadith: 205)
Imam Ibn Khuzaymah rahimahullah (311–323 AH) titles this hadith as follows: «بـاب الرخصة فى المسح على العمامة» ... The chapter regarding the concession of wiping over the turban. (Sahih Ibn Khuzaymah: 1/91, Hadith: 181)
Imam Ibn Hibban rahimahullah (d. 345 AH) says: «ذكـر الابـاحة للمرء أن يمسح على عمامته كما كـان يمسح على خفيه سواء دون الناصية» ... The explanation that it is permissible for a man to wipe only over his turban, even if he does not wipe over his forehead, just as it is permissible to wipe over the leather socks. (Sahih Ibn Hibban: 3/174, Hadith 1343)
Imam Abu Fahd ‘Abdullah bin ‘Abd al-Rahman al-Darimi rahimahullah (181–255 AH) has titled a chapter as follows: «بــاب الـمسح على العمامة» ... The chapter regarding wiping over the turban. He was also asked: Do you act upon this hadith? He replied: Yes, by Allah! (Musnad al-Darimi: 1/554, Hadith: 7370)

Evidence No. ➋ ... «عن بلال : أن رسول الله صلى الله عليه وسلم مسح على الخفين و الخمار» ... It is narrated from Sayyiduna Bilal radi Allahu anhu that the Messenger of Allah sallallahu alayhi wa sallam wiped over his leather socks and turban. (Sahih Muslim, Hadith 275)
Imam Ibn Khuzaymah rahimahullah also established from this hadith (Sahih Muslim 275) the permissibility of wiping only over the turban. (Sahih Ibn Khuzaymah: 1/91, Hadith: 180)
Imam al-Tirmidhi rahimahullah says: “Chapter: What has been narrated regarding wiping over the turban”—the narrations that have been reported about wiping over the turban. (Jami‘ al-Tirmidhi, Hadith: 101)

Evidence No. ➌ ... «عن ثوبان قال : بعث رسول الله صلى الله عليه وسلم سرية ، فأصابهم البرد ، فلما قدموا على رسول الله صلى الله عليه وسلم أمرهم أن يمسحوا على الغصائب و التساخين » ... It is narrated from Sayyiduna Thawban radi Allahu anhu that the Messenger of Allah sallallahu alayhi wa sallam sent out an army, and they experienced cold. When they returned to the Messenger of Allah sallallahu alayhi wa sallam, he instructed them to wipe over their turbans and leather socks. (Musnad al-Imam Ahmad: 5/277, Sunan Abi Dawud: 146, and its chain is authentic)
Imam al-Hakim rahimahullah (1/169) declared this hadith authentic, and Hafiz al-Dhahabi rahimahullah agreed with him. Likewise, Janab Taqi Usmani Deobandi sahib has also acknowledged the authenticity of its chain. (Dars Tirmidhi by Taqi Usmani: 1/337)

Evidence No. ➍ ... «عن المغيرة بـن شـعبة ، عـن أبيه قال : توضأ النبى صلى الله عليه وسلم ، ومسح على الخفين ، والعمامة » ... Sayyiduna Mughirah bin Shu‘bah narrates that the Prophet sallallahu alayhi wa sallam performed ablution (wudu) and wiped over his leather socks and turban. (Musnad al-Imam Ahmad: 4/248, Jami‘ al-Tirmidhi: 100)
Imam Ibn Khuzaymah rahimahullah (1514) and Imam Ibn Hibban rahimahullah (1347) have declared this hadith authentic. Likewise, Janab Taqi Usmani sahib has acknowledged the authenticity of its chain. (Dars Tirmidhi by Taqi: 1/337)
Imam al-Tirmidhi rahimahullah says: The hadith of Sayyiduna Mughirah bin Shu‘bah is hasan sahih (good and authentic). Many of the scholars among the Companions held this view. Among them are Sayyiduna Abu Bakr al-Siddiq, Sayyiduna ‘Umar al-Faruq, and Sayyiduna Anas radi Allahu anhum. This is also the view of Imam al-Awza‘i, Imam Ahmad bin Hanbal, and Imam Ishaq bin Rahuyah rahimahullah. They say that it is permissible to wipe over the turban. (Jami‘ al-Tirmidhi: under Hadith: 100)

Observe also a few reports from the Salaf:
‘Asim rahimahullah narrates: I saw Sayyiduna Anas bin Malik radi Allahu anhu urinate, then perform ablution, and wipe over his turban and leather socks. (Musannaf Ibn Abi Shaybah: 1/182, Musannaf ‘Abd al-Razzaq: 1/189, and its chain is authentic)
Abu Ghalib rahimahullah narrates: I saw Sayyiduna Abu Umamah wiping over his turban. (Musannaf Ibn Abi Shaybah: 1/21, al-Awsat by Ibn al-Mundhir: 1/468, and its chain is authentic)
Imam al-Tirmidhi rahimahullah says: I heard Jarud bin Mu‘adh narrating that he heard Waki‘ bin Jarrah rahimahullah say: The hadith of the Prophet sallallahu alayhi wa sallam makes wiping over the turban permissible. (Jami‘ al-Tirmidhi, under Hadith: 110, and its chain is authentic)