(a) It is narrated from Sayyiduna Ibn 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 his mount, in whichever direction it carried him.
(b) Abdullah bin Dinar (may Allah have mercy on him) says that Abdullah bin Umar (may Allah be pleased with them both) also used to do this.
(c) In the narration of Imam al-Shafi'i (may Allah have mercy on him): the Messenger of Allah (peace and blessings be upon him) used to offer (voluntary) prayer on his mount while travelling, wherever it faced.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2200
It is narrated from Sa'id bin Jubayr that Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) used to offer (voluntary prayer) on his mount by gestures, whichever way the mount faced, and he would say: "the Prophet (peace and blessings be upon him) also used to do this." Then he recited this noble verse: "To Allah belong the east and the west; so wherever you turn, there is the Face of Allah. Indeed, Allah is All-Encompassing, All-Knowing." [Surah al-Baqarah: 115] Then he said: This verse was revealed concerning this very matter.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2201
It is narrated from Sayyiduna Ibn Umar (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) was coming from Makkah towards Madinah seated on his mount and offering (voluntary) prayer; whichever way he faced, he kept on praying. Sayyiduna Ibn Umar (may Allah be pleased with them both) says that this noble verse was revealed concerning this very matter: "So wherever you turn, there is the Face of Allah." [Surah al-Baqarah: 115]
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2202
It is narrated from Sayyiduna Jabir bin Abdullah al-Ansari (may Allah be pleased with him) that he said: I saw the Messenger of Allah (peace and blessings be upon him) during the expedition of Anmar offering voluntary prayer on his mount while facing the east.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2203
It is narrated from al-Hasan (may Allah have mercy on him) that he saw no harm in offering voluntary prayer while driving camels, in whichever direction they faced. If he reached a verse of prostration, he would recite it and prostrate.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصلاة / 2204