Overall meaning
In general, the Sharia treats obligatory and supererogatory prayers alike; this is the default. Whatever ruling is established for one normally applies to the other. Yet a small number of texts single out one of the two with a distinct ruling. Most of these distinctions lighten the rules for voluntary prayers while keeping the obligatory prayers unchanged, and the ḥadith under discussion is one such example.

Because the Law encourages believers to perform many voluntary prayers, it grants them concessions. Thus the Prophet ﷺ would offer them while travelling on the back of his mount, wherever it faced, even if that was not toward the qiblah, indicating his bowing and prostration with a mere nod of the head. It makes no difference whether the prayer is an unrestricted supererogatory prayer, one of the regular sunnah prayers, or a prayer connected to a specific occasion. For this reason he even performed the most emphatic of the voluntary prayers—the witr—on his mount.

By contrast, the five prescribed prayers occur rarely enough that they do not overly burden the traveller, and they must be observed with full care and completeness. Hence they are not valid on a mount except in cases of necessity.

Legal inferences from the ḥadith

1. Voluntary prayers may be performed while travelling on a mount, and Ibn ʿUmar’s actual practice carries even greater weight than his mere narration of the ruling.
2. Imams Aḥmad and Abū Thawr maintained that one should face the qiblah at the beginning of the prayer. They relied on the ḥadith of Anas, which states that whenever the Prophet ﷺ wished to pray voluntarily while travelling he would first turn his camel toward the qiblah and then continue wherever it took him. The plain wording of the report is general.
3. Obligatory prayers may not be offered on a mount without necessity. The scholars explained that this is to prevent missing the qiblah, something likely to happen while riding. In genuine need—such as danger or flooding—it is permissible, as other ḥadiths attest.
4. In this context, signalling with the head stands in place of actual bowing and prostration.
5. For a person praying a voluntary prayer on a mount, his qiblah is simply the direction in which he is heading.