Hayden claimed his case was strong and indicated that he would take it to trial where he believed he would be successful.
He said that he had been at a church in Addington that evening when a gust of wind spooked his horse, causing him to fall off the horse he was riding, and for Archie's reins to come out of his grasp.
Archie then leaped over a chain fence and took off "in a terrified gallop" Hayden told the court.
Archie galloped for around 2km before he was struck on the dual carriageway of Brougham Street about 7.45pm.
Police said the complainant who was driving had not sought reparation for damage to his car. The driver received minor injuries.
Judge Somerville entered a not-guilty plea, and the case will go to trial. Hayden asked for it to be heard in Te Reo Maori, which is his legal right.
Hayden later caused a fracas in court, claiming he wanted to leave to "check his animals" but had to remain in court to sign some documents.
Afterwards, he rounded up his muzzled terrier and a newborn puppy that he put in his rucksack, and mounted Beauti-foal. He told APNZ he intended to represent himself at trial, and again reiterated that he had a strong case.
A woman who had just come out of court, asked for a lift, and he gave her a ride outside the court house to much amusement, with cars stopping traffic to take a gander, before Hayden trotted off.
Hayden appeared earlier this month in a documentary on the lives of homeless people in post-earthquake Christchurch.