Sayyiduna Abdullah bin Umar (may Allah be pleased with him) narrates that the Messenger of Allah (peace and blessings be upon him) used to offer voluntary prayers and Witr on his mount, whichever direction it faced, but he (peace and blessings be upon him) did not offer obligatory prayers on his mount.
And in it is that which indicates that Witr is not obligatory, since the Prophet, peace and blessings be upon him, did not pray the prescribed prayers on his mount in the situation in which he would perform Witr upon it.
Hadith Referenceصحيح ابن خزيمه / جماع أبواب ذكر الوتر وما فيه من السنن / 1090