The Hanafi scholars did say that wiping the back of the neck is Mustahab (recommended), although not all agreed. Some Hanafis said, it is not mustahab and some have even considered it Bid’ah.
However, it seems the strongest opinion, the opinion held by Ibn Abideen and others, is that it is Mustahab to wipe the back of the neck.
(قَوْلُهُ: وَمَسْحُ الرَّقَبَةِ) هُوَ الصَّحِيحُ، وَقِيلَ: إنَّهُ سُنَّةٌ كَمَا فِي الْبَحْرِ وَغَيْرِهِ (رد المحتار)
al-Haskafi: and wiping the neck (is Mustahab).
Ibn Abideen: His words “and wiping the neck (is Mustahab)” this is the sound opinion. Another (weaker) opinion says it is Sunnah as mentioned in al-Bahr and other than it. (Radd al-Mutaar)
(وَمَسْحُ الرَّقَبَةِ مُسْتَحَبٌّ بِظَهْرِ الْيَدَيْنِ لِعَدَمِ اسْتِعْمَالِ بِلتهِمَا، وَالْحُلْقُومُ بِدْعَةٌ. وَقِيلَ مَسْحُ الرَّقَبَةِ أَيْضًا بِدْعَةٌ (فتح القدير
Ibn Humaam: And wiping the neck is Mustahab, it is done with the back of the hands because the water on them has not been used. Wiping the throat is Bid’ah. Another (weaker) opinion says it is Bid’ah to wipe the neck too. (Fath al-Qadeer).
There is Hadith evidence to support the Hanafi opinion. However it is somewhat open to interpretation, hence the difference of opinion.
عَنْ طَلْحَةَ بْنِ مُصَرِّفٍ، عَنْ أَبِيهِ، عَنْ جَدِّهِ، قَالَ: رَأَيْتُ رَسُولَ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ يَمْسَحُ رَأْسَهُ مَرَّةً وَاحِدَةً حَتَّى بَلَغَ الْقَذَالَ – وَهُوَ أَوَّلُ الْقَفَا
“Talhah ibn Musarif narrated from his father, from his grandfather who said, ‘I saw the Messenger of Allah ﷺ wiping his head once up to his nape.'” – Abu Dawood, 132 [Weak].
This Hadith is weak according to Imam Ibn Hajr al-Asqalaani:
مَا رَوَاهُ أَحْمَدُ وَأَبُو دَاوُد مِنْ حَدِيثِ طَلْحَةَ بْنِ مُصَرِّفٍ، عَنْ أَبِيهِ، عَنْ جَدِّهِ أَنَّهُ «رَأَى النَّبِيَّ – صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ – يَمْسَحُ رَأْسَهُ، حَتَّى بَلَغَ الْقَذَالَ وَمَا يَلِيهِ مِنْ مُقَدَّمِ الْعُنُقِ». وَإِسْنَادُهُ ضَعِيفٌ كَمَا تَقَدَّمَ
What Ahmad and Abu Dawood narrated from the Hadith of Talhah ibn Musarif from his father, from his grandfather that he saw the Messenger of Allah ﷺ wiping his head up to the nape, and what is after it at the beginning of neck. Its chain is weak, as has been mentioned. (al-Talkhees al-Habeer).
There is also a narration in Imam al-Tabarani’s al-Mo’jam al-Kabeer (409), however it is weak too. Although the scholars of Ahl al-Sunnah generally accept weak Hadith for matters of Nafl, they are not obliged to accept every weak Hadith (as opposed to strong Hadith, where it is an obligation to accept), rather they may reject it if they remain unconvinced. Therefore some scholars do not accept these narrations and consider the wiping of the neck a Bid’ah, this opinion is recognised within the Madhab but it is not the soundest opinion.
Answered by Shaykh Noor ud-deen (04.01.2021)