Ibn Umar (may Allah be pleased with them both) said that the Messenger of Allah (peace and blessings be upon him) used to stone Jamrat al-Aqabah while riding, saying the takbir with each pebble. And Ibn Umar (may Allah be pleased with them both), during these days, that is, the Days of Tashriq, used to come to the Jamrahs on foot and return on foot, and he would say that the Prophet (peace and blessings be upon him) used to do the same.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9557
Ibn Umar (may Allah be pleased with them both) used to come to and go from the Jamrahs on foot during the three days after the day of sacrifice, and he would say: "the Prophet (peace and blessings be upon him) used to do this."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9558
Likewise (through another chain).
Abd al-Rahman bin Abdullah bin Umar (may Allah be pleased with them) narrated this hadith from his father and his uncle, but he did not mention "the three days", and the narration of al-Ashyab also does not explicitly state the three.
Imam al-Shafi'i (may Allah have mercy on him) said: Since he stoned riding on the day of sacrifice because his riding continued on from Muzdalifah, it would be analogous that he stoned riding on the day of departure because his riding continued into his departure. The Shaykh said: This is also the view of Ata bin Abi Rabah (may Allah have mercy on him).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9559
Ata (may Allah have mercy on him) said: Stoning the Jamrahs is two days riding and two days walking. The Shaykh (may Allah have mercy on him) said: If the hadith of al-Umari is sound, it is more worthy of being followed.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9560
Al-Qasim said: People used to go to and from stoning the Jamrahs on foot, and Sayyiduna Mu'awiyah (may Allah be pleased with him) was the first person to ride.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9561
Jabir bin Abdullah (may Allah be pleased with them both) used to dislike riding to any of the Jamrahs except out of necessity.
This is how I found it in my book; a man has dropped out of its chain between Ibrahim and Ata, and the narration of Ibn Uyaynah is more correct.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9562