(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