Answer
I say, and with God's success: It is obligatory to wash the mouth and nose during the full ablution (ghusl), unlike washing them during ablution (wudu), which is recommended but not obligatory; as He, Glory be to Him, said: {And if you are in a state of janabah, then purify yourselves} (Al-Ma'idah: 6): meaning purify your bodies. Therefore, everything that can be purified must be washed, and the inside of the mouth and nose can be washed, as they are washed both as a habit and as an act of worship, as a voluntary act in ablution and as an obligation in janabah. This is because the mouth is inward from one aspect and outward from another, in terms of the sensation when the mouth closes and opens, and in terms of the ruling regarding the swallowing of the saliva by the fasting person, where its ruling is like that of the inward, as it does not break the fast. This is a sign of it being inward, and when something enters the mouth, its ruling is like that of the outward, as it breaks the fast. This is a sign of it being outward, thus it is considered inward in ablution and outward in ghusl; because the wording in it is in the form of exaggeration {Then purify yourselves}. And from Ibn Abbas (may Allah be pleased with him): "If a man performs ghusl from janabah and does not rinse his mouth or sniff water, he should repeat the ablution, but if he leaves that in ablution, he does not repeat it," in the narrations 1: 13. And Al-Tahanawi said in I'laa al-Sunan 1: 183: The hadith is good and acceptable for argument, and it has a correct supporting narration from the mursal of Ibn Sirin. From Ibn Sirin, he said: "The Messenger of Allah (peace be upon him) established the act of sniffing water in janabah three times," in Sunan al-Daraqutni 1: 115, and Al-Bayhaqi approved it and authenticated it as in I'laa al-Sunan 1: 183. And from Ali (may Allah be pleased with him), he said (peace be upon him): "Whoever leaves a spot of hair on his body from janabah that water does not reach, he will be punished like this and that with fire," in Musnad Ahmad 1: 101, and Musannaf Ibn Abi Shaybah 1: 96, and Sunan al-Bayhaqi al-Kabir 1: 227, and Sunan Ibn Majah 1: 196, and Al-Mu'jam al-Saghir 2: 179, and Al-Ahadith al-Mukhtarah 2: 74. Al-Khattabi said: "One may use this as an argument for those who make sniffing water obligatory in janabah due to the hair inside the nose," refer to: I'laa al-Sunan 1: 180, and Tabyin al-Haqaiq 1: 13, and Sharh al-Wiqayah p. 91, and Allah knows best.