It is permissible to offer voluntary prayers atop one’s mount when travelling, no matter what direction it is facing
وَحَدَّثَنَا عَمْرُو بْنُ سَوَّادٍ، وَحَرْمَلَةُ، قَالاَ أَخْبَرَنَا ابْنُ وَهْبٍ، أَخْبَرَنِي يُونُسُ، عَنِ ابْنِ شِهَابٍ، عَنْ عَبْدِ اللَّهِ بْنِ عَامِرِ بْنِ رَبِيعَةَ، أَخْبَرَهُ أَنَّ أَبَاهُ أَخْبَرَهُ أَنَّهُ، رَأَى رَسُولَ اللَّهِ صلى الله عليه وسلم يُصَلِّي السُّبْحَةَ بِاللَّيْلِ فِي السَّفَرِ عَلَى ظَهْرِ رَاحِلَتِهِ حَيْثُ تَوَجَّهَتْ .
'Abdullah b. 'Amir b. Rabi'a has reported on the authority of his father that he had seen the Messenger of Allah (ﷺ) observing Nafl player at night on a journey on the back of his ride in whichever direction it turned its face.