I accompanied the Messenger of Allah (ﷺ) on eighteen journeys and I never saw him fail to pray two rak'ahs when the sun had passed the meridian before offering the noon prayer.

I accompanied Ibn 'Umar on the way (on a journey). He led us in two rak'ah's of (the noon) prayer. Then he proceeded and saw some people standing. He asked: What are they doing ? I replied: They are glorifying Allah (i.e. offering supererogatory prayer). He said: If I had offered the supererogatory prayer (while travelling), I would have completed prayer, my cousin. I accompanied the Messenger of Allah (ﷺ) during the journey, he did not pray more than two raka'at until his death. I also accompanied Abu Bakr, and he prayed two raka'at and nothing more until he died. I also accompanied 'Umar, and he prayed two raka'at and nothing more until he died. I also accompanied 'Uthman, and he prayed two raka'at and nothing more until he died. Indeed Allah, the Exalted, said: Certainly you have in the Messenger of Allah an excellent exemplar

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.

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.

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

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.