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The pair were two of the about 80 people who went along to the group's open day at its grounds in Hayle St, where children of all ages and abilities were given the opportunity to be taken for a leisurely pony or horse ride around a short circuit.
Ms Tangney, who has cerebral palsy, fondly remembered her time horse riding when she was young, and wanted to share that experience with Rome.
"I used to come up to Riding for the Disabled when I was at primary school, so I thought it would be good for the kids to come up and have a look and see what it's all about.
"It was something I could do that able-bodied people could do as well.
"It was good to be able to ride and help look after the horses, and meet other people with disabilities as well."
She said Rome, who was led around on Spice the pony, thoroughly enjoyed himself and said his ride was "so cool".
North Otago Riding for the Disabled president Deborah Lord said the group, founded in 1980, had 22 volunteers and seven ponies and horses, which were looked after on site.
Holding open days was important for the group in terms of bringing the community together, she said.
"We like to give the regular riders a chance to bring their parents or other caregivers and family to see what they do at Riding for the Disabled, and let other children from the community to come and have a ride on our ponies.
"We like to think it helps confidence, physical co-ordination and social skills ... We hope they have a lot of fun with it too."