It is permissible to offer voluntary prayers atop one’s mount when travelling, no matter what direction it is facing Sahih Muslim 700 c
Arabic hadith text
وَحَدَّثَنِي عُبَيْدُ اللَّهِ بْنُ عُمَرَ الْقَوَارِيرِيُّ، حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ، عَنْ عَبْدِ الْمَلِكِ بْنِ أَبِي سُلَيْمَانَ، قَالَ حَدَّثَنَا سَعِيدُ بْنُ جُبَيْرٍ، عَنِ ابْنِ عُمَرَ، قَالَ كَانَ رَسُولُ اللَّهِ صلى الله عليه وسلميُصَلِّي وَهُوَ مُقْبِلٌ مِنْ مَكَّةَ إِلَى الْمَدِينَةِ عَلَى رَاحِلَتِهِ حَيْثُ كَانَ وَجْهُهُ - قَالَ - وَفِيهِ نَزَلَتْ { فَأَيْنَمَا تُوَلُّوا فَثَمَّ وَجْهُ اللَّهِ}
Translation
Ibn 'Umar reported that the Messenger of Allah (ﷺ) used to say prayer on his camel while coming from Mecca to Medina, in whatever direction his face had turned; and its was (in this context) that this verse was revealed
" So whether you turn thither is Allah's face" (ii. 115).