Sayyiduna Anas bin Malik (may Allah be pleased with him) used to perform Hajj on a mount, and he was not miserly, and he narrated that the Messenger of Allah (peace and blessings be upon him) also performed Hajj on a mount, and that same mount also carried his baggage.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 8651