The polar blast icing the South Island today looks set to stay for the rest of the week, forecasters have warned.

A dusting of light snow has already settled on the Port Hills above Christchurch this morning, as temperatures struggle to reach above 6C.

A severe weather watch has been issued by MetService, which has forecast snow to fall as low as 100m in the South Island today.

Queenstown Lakes District Council this morning received reports of "several" stranded vehicles after a black ice alert on Littles Rd and at Dalefield.

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"The grit trucks are on the job but if possible, avoid travelling in the area until things warm up. There's a danger of black ice everywhere," the council warned. The slippery conditions were too much for one motorist whose car ended up in Otago Harbour this morning, the Otago Daily Times reported.

Ice and snow led to a 10am start for all DKA kindergartens, primary and intermediate schools in Dunedin, and for several high schools as well.

Three schools - Halfway Bush, East Otago High and Flag Swamp Primary - are closed for the day.

Otago Regional Council warned that some bus services are disrupted.

The NZ Transport Agency (NZTA) has warned of surface flooding at Mossburn, and icy and slippery road conditions for many southern routes. A caution has been issued for icy conditions at Porters Pass.

Sleety showers have residents of southern and eastern cities and towns shivering today.

And they don't have any respite to look forward to for the rest of the week, MetService meteorologist Stephen Glassey said.

While a ridge of high pressure moving in from the west will clear the showers and bring clear skies, temperatures will stay extremely low, forecasters say.

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Most South Island areas will wake tomorrow to "severe" frosts, Mr Glassey said.

Inland Canterbury and Central Otago will likely drop to -5C overnight.

The worst hit areas, Mr Glassey said, will likely be Alexandra, Cromwell and Clyde which cold drop as low as -8C.

Motorists need to be aware of the dangers of black ice tomorrow, especially ice from melted snow or rain freezes on the roads overnight, Mr Glassey warned.

Single digit temperatures are forecast for most southern areas this week.

On Friday, another southerly change is expected to move over the South Island and likely bring more showers and low temperatures.

It's good news for the ski fields, however, which have had a slow start to the season.

Mt Hutt Ski Area in Canterbury is open, with a fine day and minimum of 80cm snow base, as is Porters Ski Area for its first day of the season.

Queenstown's Cardona Alpine Resort and Coronet Peak Ski Area are both open.