Bubbles was the park's last remaining ostrich, and had been a resident there for 10 years.
Mr Horan said he was a bit of a favourite among the staff, and would be missed.
"He loved the audience and would steal hats off people, and sunglasses - he had quite a collection of them," he said.
"He was one of the first animals that staff see when we drive up the staff entrance. He would do his dance, and they would have to reply by winding the windows down and saying, 'hello Bubbles', and then he would be happy."
Mr Horan said the park had suffered severe wind damage, including the loss of two enclosures, as well as whares at the Ko Tane Cultural Experience which were crushed by trees, and a perimeter fence at the otter enclosure.
"We all pitched in and we were operational by Wednesday just after lunch - running on generators, but we were open," Mr Horan said.
"We're just doing the final clean-up now, with the last of the trees that have come down and making sure everything's tip-top again."
Mr Horan said no decision had been made on whether to replace Bubbles.
"At this stage we're taking a big deep breath," he said. "We have lost not only an ostrich but two enclosures, we've had to rehouse birds.
"Working out where we go from here, whether we get another ostrich or a different exhibit, we're not quite sure yet."