It was the practice of the Prophet (peace and blessings be upon him):
"When he (peace and blessings be upon him) went to stone the Jamarat, he would walk on foot, going and returning."
Hadith Referenceصحیح الجامع الصغیر / حرف الكاف / 4735
Hadith Gradingالألبانی:صحيح
Hadith Takhrij[ت] عن ابن عمر. الصحييحة ٢٠٧٢: حم، د.