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Snow was already falling north of Wellington, over the Rimutaka Hill, Ms Moes said.
There was good news for Northland however, with showers finally easing today after about a week of rain, she said.
Meanwhile, the icy conditions have affected a number of roads around the country.
Snow flurries closed State Highway 1, the Desert Road, overnight, but it had now reopened.
The New Zealand Transport Agency (NZTA) has urged motorists to take care on the road and drive to winter conditions.
Snow has also closed SH2 over the Rimutaka Hill north of Wellington.
AA Roadwatch has warned drivers to take extreme care on several South Island roads that are affected by ice and snow.
Road closures and cautions:
* SH2 over the Rimutaka Hill - closed due to snow;
* SH1, Desert road - caution, snow;
* SH1, Brynderwyn Hills - closed due to a slip;
* Glenorchy-Queenstown Rd, Mount Creighton - caution, black ice;
* Glenorchy-Queenstown Rd, Fernhill - caution, black ice;
* Arthurs Point Rd - caution, black ice;
* Malaghans Rd, Arrowtown - caution black ice;
* SH94, Mossburn to Te Anau - caution, ice;
* SH85, Kyeburn to Palmerston - caution, snow;
* SH87, Outram to Kyeburn - caution, snow;
* SH1, Dunedin to Waikouaiti - caution, snow;
* Crown Range Rd, Crown Terrace - caution, snow;
* SH6, Kingston to Lumsden - caution, snow;
* Coronet Peak Rd - caution, snow;
* SH8, Fairlie to Omarama - caution, snow and ice; and
* SH94, Te Anau to Milford Sound - caution, snow.
(source: AA Roadwatch)
Temperatures for the day:
* Whangarei: high of 13C, low of 6C
* Auckland: high of 12C, low of 4C;
* Hamilton: high of 10C, low of -1C;
* Tauranga: high of 11C, low of 3C;
* Wellington: high of 8C, low of 5C;
* Christchurch: high of 9C, low of 5C; and
* Dunedin: high of 8C, low of 6C.
(source: MetService)
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