Under what circumstances is it permissible to ride the sacrificial animal (Hady)?
Chapter on Ransom (Fidyah) and Penalty for Hunting
Al-Mughni
Book of Hajj
Primary text
Riding the Hady is permissible only when there is a necessity and in a manner that does not cause harm to the animal. Ahmad, Al-Shafi'i, Ibn al-Mundhir, and the People of Opinion hold this view, citing the statement of the Messenger of Allah (peace be upon him): 'Ride her honorably when necessity compels you until you find another mount' (Reported by Abu Dawud). The basis is that the right of the needy is attached to the animal, thus prohibiting riding without necessity, similar to their ownership rights.
Supporting text
Regarding riding when there is no need, there are two narrations. One view states it is not permissible based on the necessity constraint mentioned above. The second view permits it, based on the reports from Abu Hurayrah and Anas that the Messenger of Allah (peace be upon him) saw a man leading a Hady and commanded him to ride it, and upon the man's hesitation due to it being a Hady, the Prophet commanded him again to ride it (Agreed upon hadith).