The Prophet ﷺ used to offer (Nawafil) prayers on his Rahila (mount) facing its direction by signals, but not the compulsory prayer. He also used to pray witr on his (mount) Rahila.  

كَانَ النَّبِيُّ ﷺ يُصَلِّي فِي السَّفَرِ عَلَى رَاحِلَتِهِ حَيْثُ تَوَجَّهَتْ بِهِ يُومِئُ إِيمَاءً صَلاَةَ اللَّيْلِ إِلاَّ الْفَرَائِضَ وَيُوتِرُ عَلَى رَاحِلَتِهِ  

Narrated ʿAbdullah bin Amir that his father had told him that he had seen the Prophet ﷺ praying Nawafil at night on the back of his Mount on a journey, facing whatever direction it took.  

أَخْبَرَهُ أَنَّهُ رَأَى النَّبِيَّ ﷺ صَلَّى السُّبْحَةَ بِاللَّيْلِ فِي السَّفَرِ عَلَى ظَهْرِ رَاحِلَتِهِ حَيْثُ تَوَجَّهَتْ بِهِ  

We went to receive Anas bin Malik when he returned from Sham and met him at a place called 'Ainat- Tamr. I saw him praying riding the donkey, with his face to this direction, i.e. to the left of the Qibla. I said to him, "I have seen you offering the prayer in a direction other than that of the Qibla." He replied, "If I had not seen Messenger of Allah ﷺ doing it, I would not have done it."  

اسْتَقْبَلْنَا أَنَسًا حِينَ قَدِمَ مِنَ الشَّأْمِ فَلَقِينَاهُ بِعَيْنِ التَّمْرِ فَرَأَيْتُهُ يُصَلِّي عَلَى حِمَارٍ وَوَجْهُهُ مِنْ ذَا الْجَانِبِ يَعْنِي عَنْ يَسَارِ الْقِبْلَةِ فَقُلْتُ رَأَيْتُكَ تُصَلِّي لِغَيْرِ الْقِبْلَةِ فَقَالَ لَوْلاَ أَنِّي رَأَيْتُ رَسُولَ اللَّهِ ﷺ فَعَلَهُ لَمْ أَفْعَلْهُ رَوَاهُ ابْنُ طَهْمَانَ عَنْ حَجَّاجٍ عَنْ أَنَسِ بْنِ سِيرِينَ عَنْ أَنَسٍ ؓ عَنِ النَّبِيِّ ﷺ