Narrated 'Amir bin Rabi`a
I saw the Prophet (ﷺ) on his Mount praying Nawafil by nodding his head, whatever direction he faced, but Allah's Messenger (ﷺ) never did the same in offering the compulsory prayers.
Narrated Salim
At night `Abdullah bin `Umar used to offer the prayer on the back of his animal during the journey and never cared about the direction he faced. Ibn `Umar said, "Allah's Messenger (ﷺ) used to offer the optional prayer on the back of his Mount facing any direction and also used to pray the witr on it but never offered the compulsory prayer on it."
Narrated Jabir bin `Abdullah
The Prophet (ﷺ) used to pray (the Nawafil) on his Mount facing east and whenever he wanted to offer the compulsory prayer, he used to dismount and face the Qibla.