The Carriage Rider is a position in the Shrek films. They help guide the horses who are pulling the carriage.
During the beginning, an unnamed dwarf rides the Onion Carriage from the first film. He helps Shrek and Fiona travel to Far Far Away, and even got irritated by Donkey's impatience. Eventually they make it to the kingdom, where he payed a man to clean a horse and parked the car. However, he was not seen again after doing so.
In the alternate reality, two witches are riding a cage containing Shrek. This carriage was also being pulled by an abused Donkey, who also takes role as the radio.