Reference: Majmoo’ Fataawa wa Rasaa.il Ibn ‘Uthaymeen – Vol.16, Page 235
Question: [On the day of ‘Eed] is it from the Sunnah to go to the place of prayer on foot, or by transport?
Response: [On the day of ‘Eed] it is from the Sunnah to go [to the place of prayer] on foot, unless there is a need to go by transport – in which case there is no harm in doing so.