Praying on a riding animal

Sayyiduna Ya'la bin Umayyah (may Allah be pleased with him) narrated: The Prophet (peace and blessings be upon him) was on a journey when it rained; there was wetness beneath us and rain above us, and the place was narrow. The time for prayer came. The Prophet (peace and blessings be upon him) ordered Sayyiduna Bilal (may Allah be pleased with him), and he gave the adhan and the iqamah. The Prophet (peace and blessings be upon him) went forward and prayed on his mount, and the people prayed on their mounts, by gestures; he would lower himself more for prostration than for bowing. (Allamah al-Haythami says:) I say:
Imam Abu Dawud recorded this as a narration of Sayyiduna Ya'la bin Murrah (may Allah be pleased with him), and here it is reported from Sayyiduna Ya'la bin Umayyah.
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir; its chain is the chain of Imam Abu Dawud, and its narrators have been declared trustworthy, except that Imam Abu Dawud said:
This narration is gharib (unusual); the narrator Umar bin al-Rammah is alone in reporting it.

Alqamah bin Abdullah al-Muzani reports this statement of his father: The Prophet (peace and blessings be upon him) said: "When you are among reeds (that is, in a reed-covered area), or snow (that is, a snowy area), or mud, and the time for prayer comes (and the prayer cannot be offered on the ground), then pray by gestures."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir and al-Mu'jam al-Awsat; its chain contains a narrator, Muhammad bin Qada', and he is da'if (weak).

Sayyiduna Amr bin Ya'la (may Allah be pleased with him) narrated: I was present at the time of an obligatory prayer while we were riding our mounts with the Prophet (peace and blessings be upon him). The Prophet (peace and blessings be upon him) led us in prayer: he went ahead of us, he led us, and we prayed on our mounts.
Imam al-Bazzar recorded it; its chain contains a narrator, Abd al-A'la bin Amir, and he is da'if (weak).

Anas bin Sirin narrated: We were coming from Kufah with Sayyiduna Anas bin Malik (may Allah be pleased with him), until, when we reached Atit, the place was one where there was mud. So Sayyiduna Anas (may Allah be pleased with him) offered the obligatory prayer while on his mount, and then he said: "Before today I have never offered an obligatory prayer on a mount."
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir, and its narrators are thiqat (trustworthy).

A woman named Azzah, who was one of the early women, narrated: Sayyiduna Abu Bakr addressed us in a sermon and said: "Do not pray on bardha'ahs (a pad placed on the back of a mule or donkey, as a saddle is placed on the back of a horse)!"
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir, and its narrators are thiqat (trustworthy) if Azzah was a Companion, which is what appears from the statement of Abu Hazim.

Sayyiduna Abu Musa al-Ash'ari reports from the Prophet (peace and blessings be upon him): "During a journey, prayer on the back of a mount is to be offered like this, like this."
Imam Ahmad and Imam al-Tabarani in al-Mu'jam al-Awsat recorded it; its chain contains a narrator, Yunus bin al-Harith, whom Imam Ahmad and others declared da'if (weak), while Ibn Hibban, Abu Ahmad Ibn Adi and, according to one report, Yahya bin Ma'in declared him thiqah (trustworthy).

Sayyiduna al-Hirmas bin Ziyad (may Allah be pleased with him) narrated: I saw the Prophet (peace and blessings be upon him) praying while riding a camel, facing towards Syria.
Imam Ahmad and Imam al-Tabarani in al-Mu'jam al-Kabir recorded it; its chain contains a narrator, Abdullah bin Waqid al-Harrani, whom Imam Ahmad and, according to one report, Yahya bin Ma'in declared thiqah (trustworthy). Imam Bukhari (may Allah have mercy on him) says: People abandoned him; a group declared this narrator da'if (weak).

Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with him) and Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) narrated: The Prophet (peace and blessings be upon him) would offer voluntary prayer on his mount whichever direction it faced; he prayed by gestures and would lower himself more for prostration than for bowing. (Allamah al-Haythami says:) I say: The hadith narrated from Sayyiduna Abdullah bin Umar is in the Sahih in abridged form, and the hadith narrated from Sayyiduna Abu Sa'id al-Khudri (may Allah be pleased with him) was recorded by Imam Ahmad and Imam al-Bazzar; the chain of both contains a narrator, Muhammad bin Abi Layla, about whom there has been criticism.

Sa'id bin Jubayr narrated: Sayyiduna Abdullah bin Umar would offer voluntary prayer on his mount; when he wanted to offer witr, he would dismount from the mount and offer witr on the ground.
Imam Ahmad recorded it, and its narrators are the narrators of the Sahih.

Sayyiduna Shuqran, the freed slave of the Prophet (peace and blessings be upon him), narrated: I saw with my own eyes the Prophet (peace and blessings be upon him) riding a donkey, heading towards Khaybar, and he prayed by gestures.
Imam Ahmad and Imam al-Tabarani in al-Mu'jam al-Kabir and al-Mu'jam al-Awsat recorded it; its chain contains a narrator, Muslim bin Khalid al-Zanji, whom Imam Ahmad and others declared da'if (weak), while Imam al-Shafi'i, Ibn Hibban and Imam Abu Ahmad bin Adi declared him thiqah (trustworthy).

Sayyiduna Sa'd bin Abi Waqqas (may Allah be pleased with him) narrated: I saw the Prophet (peace and blessings be upon him) offering voluntary prayer on his mount whichever direction it faced, and he did not do so in the obligatory prayer.
Imam al-Bazzar recorded it; its chain contains a narrator, Dirar bin Surad, and he is da'if (weak).

Sayyiduna Abu Umamah (may Allah be pleased with him) narrated: The Prophet (peace and blessings be upon him) would offer witr on his camel.
Imam al-Tabarani recorded it in al-Mu'jam al-Kabir; its chain contains a narrator, al-Ala' bin Kathir al-Laythi, and he is extremely da'if (weak).