Keep the winter woolies out - more snow is coming.

The MetService says the "decent dump'' of snow seen over the South Island overnight and this morning would see even more fall tonight and tomorrow morning.

Parts of the North Island will also get snow over the next few hours, with road snowfall warnings issued for the Napier-Taupo Road on State Highway 5, Desert Road (SH1) and Rimutaka Hill.

Other road snowfall warnings have been issued for Lewis Pass, Arthur's Pass, Porter's Pass, Lindis Pass, Crown Range Road, Milford Road and the Dunedin to Waitati Highway.

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Anyone planning to travel along those roads is being urged to monitor warnings, regular updates and weather conditions before heading out.

Active showers have moved over the Auckland region this afternoon and were also headed towards Northland.

"A few more areas of concern for the rest of the day as a front tracks across the North Island,'' MetService said.

Meanwhile, further south, several roads have been closed or affected by bad weather conditions.

The NZ Transport Agency is keeping a running list of roads affected by snow and heavy rain, particularly in the South Island.

In Otago, SH85 Ranfurly to Omakau had been affected by snow and ice and was closed as a result.

Those travelling on SH6 Queenstown to Cromwell were being cautioned about icy surfaces and snow falling on SH94 Te Anau to Milford Sound was also a cause to take extra care while driving.

Dozens of schools had been shut today due to snow.

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The Ministry of Education said 11 schools and 17 early childhood centres had been closed in the South Island and was affecting almost 3800 students and 280 children linked to childcare centres.

Parents were being told to keep up to date about via their respective school's social media pages.

More snow is expected to fall over the South Island tonight.

The wintry blast overnight and this morning has already shut off roads and caused a number of crashes, resulting in delayed starts for schools in Dunedin and across the rest of Otago.

MetService meteorologist Kyle Lee said the worst of the southerly front - which brought snow overnight and early today - was over, but isolated flurries could continue in some areas all day.

Another front was forecast to come through tonight, bringing with it more snow.

Lee said it was expected to fall above 700m, but could fall as low as 300m in some spots.

"We are expecting another dump,'' he said.