While travelling the Messenger of Allah ﷺ would pray voluntary prayer on his riding beast in whatever direction it turned; and he would observe witr prayer, but he did not offer the obligatory prayers upon it.  

كَانَ رَسُولُ اللَّهِ ﷺ يُسَبِّحُ عَلَى الرَّاحِلَةِ أَىَّ وَجْهٍ تَوَجَّهَ وَيُوتِرُ عَلَيْهَا غَيْرَ أَنَّهُ لاَ يُصَلِّي الْمَكْتُوبَةَ عَلَيْهَا  

When the Messenger of Allah ﷺ was on a journey and wished to say voluntary prayer, he made his she-camel face the qiblah and uttered the takbir (Allah is most great), then prayed in whatever direction his mount made his face.  

أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ إِذَا سَافَرَ فَأَرَادَ أَنْ يَتَطَوَّعَ اسْتَقْبَلَ بِنَاقَتِهِ الْقِبْلَةَ فَكَبَّرَ ثُمَّ صَلَّى حَيْثُ وَجَّهَهُ رِكَابُهُ  

I saw the Messenger of Allah ﷺ praying on a donkey while he was facing Khaibar.  

أَنَّهُ قَالَ رَأَيْتُ رَسُولَ اللَّهِ ﷺ يُصَلِّي عَلَى حِمَارٍ وَهُوَ مُتَوَجِّهٌ إِلَى خَيْبَرَ  

The Messenger of Allah ﷺ sent me on some business, and when I came to him he was praying on (the back of) his riding beast (moving) towards the east and making the prostration lower than the bowing.  

بَعَثَنِي رَسُولُ اللَّهِ ﷺ فِي حَاجَةٍ قَالَ فَجِئْتُ وَهُوَ يُصَلِّي عَلَى رَاحِلَتِهِ نَحْوَ الْمَشْرِقِ وَالسُّجُودُ أَخْفَضُ مِنَ الرُّكُوعِ