Kings rode horses; poor people rode donkeys. The irony of Palm Sunday is that Jesus rode not only a donkey, but is described as "humble, and mounted on a donkey" (Matthew 21:5), even as the people hailed him as the son of the mighty king David, no doubt in the hope that he would exercise his power to drive out the Romans. Applying the Zechariah verse to Jesus' entry into Jerusalem was clearly meant to exemplify the true nature of Jesus' ministry.
9 Rejoice greatly, O daughter Zion!
Shout aloud, O daughter Jerusalem!
Lo, your king comes to you;
triumphant and victorious is he,
humble and riding on a donkey,
on a colt, the foal of a donkey.
New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org