It is narrated from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) used to offer voluntary prayer on the mount, whichever direction his face was turned, and he would also pray witr on it; however, he did not offer the obligatory prayer on the mount.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2218
It is narrated from Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) that the Prophet (peace and blessings be upon him) used to offer voluntary prayer on his mount facing the east. When he intended to offer the obligatory prayer, he would dismount, face the qiblah and offer it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2219
It is narrated from Sayyiduna Amir bin Rabi'ah (may Allah be pleased with him) that he said: I saw the Messenger of Allah (peace and blessings be upon him) offering voluntary prayer on his mount. He was making gestures with his head and was not paying attention to the qiblah. But he (peace and blessings be upon him) did not do this in the obligatory prayers.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2220
It is narrated from Sayyiduna Sahl bin al-Hanzaliyyah (may Allah be pleased with him) that he said: We travelled with the Messenger of Allah (peace and blessings be upon him) in an army; then he mentioned the complete hadith. In it there is also that the Messenger of Allah (peace and blessings be upon him) said: "Who will guard us tonight?" Sayyiduna Unays bin Abi Marthad al-Ghanawi (may Allah be pleased with him) said: O Messenger of Allah! I will. He (peace and blessings be upon him) said: "Go to this mountain pass until you reach its top, and do not come down at all except to pray or to relieve yourself."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2221
(a) It is narrated from Ata' bin Abi Rabah that he asked the Mother of the Believers Sayyidah Aishah (may Allah be pleased with her): Have women been given a concession to pray on riding animals? She said: Women have not been given permission, neither in any hardship nor in normal circumstances.
(b) Muhammad said: This concerns the obligatory prayer.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2222
It is narrated from Sayyiduna Ibn Umar (may Allah be pleased with them both) that during travel he would make even the sick dismount from their mounts so that they would offer the obligatory prayer on the ground.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2223
(a) It is narrated from Amr bin Uthman bin Ya'la that the Prophet (peace and blessings be upon him) and his Companions (may Allah be pleased with them) passed through a narrow pass; rain was falling from above and there was wetness below (the narrator is unsure whether the word was 'al-sama'' or 'al-billah'). The time of prayer came; he (peace and blessings be upon him) ordered the mu'adhdhin, and he called the iqamah. Then the Messenger of Allah (peace and blessings be upon him) came forward on his mount and led them in prayer. He (peace and blessings be upon him) was praying by gestures, making the prostrations lower than the bowing. In the narration of Abu Abdullah, Yahya (may Allah have mercy on him) says that perhaps he said: The enemy was above them and the wetness below them.
(b) Its chain is weak; some of its narrators are not reliable, because of which their hadith is not authentic.
It is also possible that this (manner of prayer) was due to the severity of fear.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2224