Canterbury one of my favorite places in the world. Checked the annual climate, but don't see that it gets cold enough to freeze the ponds? Here across the big pond, we go by water temperature. I stop feeding my fish when the water temp is consistently below 10C or 50F. I stop my water falls and filtration when air temps are close to freezing and add aerators and a deicer. If your water doesn't freeze, you can run your pumps all year long and even feed them I suppose. When it's colder my fish aren't that interested in eating much.
I run my ponds and pumps all year round since 1991, in Canada, where temps can fall below -40 Celsius and water temps get close to freezing, bottom pond can get lots of thick ice. Running water year round keeps ice thinner in upper connecting ponds. Two of my oldest Koi have been outside and alive since 1991. Everybody doing just great after one of the longest hardest winters I can remember in years... I am pretty sure your koi will be just fine as your winters are very short. America has some wild koi now in some lakes, as KOI are "cold water fish" and should be fine if your koi are healthy. Many people now wintering koi all over.