Hadith: The Messenger of Allah (may Allah's peace and blessings be upon him) used to offer voluntary prayer on the back of his riding beast (camel), whatever direction it went. He would nod his head. Ibn ‘Umar would do so as well

عن عبد الله بن عمر رضي الله عنهما «أن رسول الله صلى الله عليه وسلم كان يُسَبِّحُ على ظَهرِ رَاحِلَتِه حَيثُ كان وَجهُهُ، يُومِئُ بِرَأسِهِ، وكَان ابنُ عُمرَ يَفعَلُهُ». وفي رواية: «كان يُوتِرُ على بَعِيرِه». ولمسلم: «غَيرَ أنَّه لا يُصَلِّي عَليهَا المَكتُوبَة». وللبخاري: «إلا الفَرَائِض».
[صحيح] - [الروايات الثلاثة الأولى متفق عليها. الرواية الرابعة: رواها البخاري]

Abdullāh ibn ‘Umar (may Allah be pleased with him) reported that the Messenger of Allah (may Allah's peace and blessings be upon him) used to offer voluntary prayer on the back of his riding beast (camel), whatever direction it went. He would nod his head. Ibn ‘Umar would do so as well. Another version reads: "He used to perform Witr on top of his camel." A version by Muslim adds: "But he did not offer the obligatory prayer on top of it." A version by Al-Bukhāri states: "…except for the obligatory prayers."
[Authentic hadith] - [Narrated by Bukhari - Narrated by Bukhari & Muslim]

Explanation

The Messenger of Allah (may Allah's peace and blessings be upon him) used to perform the voluntary prayer only on the back of his riding beast, regardless of its direction. He would gesture with his head instead of bowing and prostration and did not bother to dismount to bow, prostrate himself, or face the Qiblah. This applies equally to the voluntary prayers, the regular Sunnah prayers, and other prayers fir specific reasons. The Prophet (may Allah's peace and blessings be upon him) however, did not do so when performing the obligatory prayers. In addition, he would offer the Witr prayer on the back of his camel.