The most emphatically stressed of these regular sunnah prayers are the two rakʿahs before Fajr. ʿĀʾishah (may Allah be pleased with her) said, “The Prophet was never more diligent in maintaining any supererogatory prayer than he was in maintaining the two rakʿahs before dawn.” Agreed upon. He also said, “The two rakʿahs of Fajr are better than the whole world and everything in it.” For that reason the Prophet was unfailingly constant in observing them, along with witr, whether he was resident or traveling.
As for the other regular sunnah prayers besides the two rakʿahs of Fajr and witr, there is no report that the Prophet offered any of those sunnah prayers while on a journey.
When Ibn ʿUmar (may Allah be pleased with them) was asked about the sunnah of ẓuhr during travel, he replied, “If I were going to pray extra, I would have completed the obligatory prayer in full.”
Ibn al-Qayyim said, “His practice while traveling was to limit himself to the obligatory prayers, and no authentic report records that he performed the sunnah prayers before or after the obligatory ones except for witr and the two rakʿahs of Fajr.”