Snow has made roads impassable in many areas of both islands.
MetService head forecaster Peter Kreft told NZPA the polar blast was "of the order of a 50 year" event and warned it could last for several more days.
"It's a once in many decades event. We are probably looking at something like - in terms of extent and severity, maybe 50 years," he said.
The level of snow that fell in Wellington had not been seen since at least the 1970s, he said.
The front was bringing snow to parts of the country which did not usually see it and even Auckland would not be spared.
"I'd be surprised if over the next few days people didn't see sleet [in Auckland]," he said.
NZ Post warned mail deliveries could be delayed in many areas because of the snow.
Dunedin Airport was also closed this morning with about 150 passengers forced to stay there overnight after four flights were grounded.
The airport would remain closed until the weather improved and ice on the runway was able to melt, its chief executive, John McCall, told Radio New Zealand.
Passengers were also left stranded at Queenstown Airport and a number have flights had been cancelled in and out of Christchurch Airport this morning.
Christchurch Airport advised people to check with their airline before going to the airport.
Many schools across the South Island were closed for the day.
Christchurch police urged people to check conditions before travelling and drive to the conditions.
"We are asking the public to stay at home and delay all non-essential travel if they do not think they can travel safely in their local conditions," Inspector Al Stewart, Canterbury road policing manager said.
Snow cut power to a few hundred people in Christchurch and central Canterbury overnight, lines company Orion said.
Crews were working as "fast as possible" to restore power to parts of Sumner, Tai Tapu and Springston, Orion manager Rob Jamieson said.
"In general the network is coping pretty well, with fewer issues at this stage than we experienced during the July snow storm.
"However, it's likely to be a longer event this time, and our crews are ready to respond quickly to any further issues and make any repairs needed," Mr Jamieson said.
Canterbury University, Christchurch Polytechnic Institute of Technology, and Otago University's Christchurch campus were closed for the day and Environment Canterbury said all Christchurch metro bus services had been suspended until further notice.
Canterbury Earthquake Recovery Authority closed access to the city's quake-damaged red zone and would reassess the situation at 11am.
Southland Civil Defence was advising people to stay at home and avoid all non-essential travel this morning.
"People will have to be patient. If you do have to travel, you need to think about how you get home again," Civil Defence manager Neil Cruickshank said.
Power had been cut to parts of the south coast of Southland from Fortrose to Waikawa, he said.
Southland Federated Farmers president Rod Pemberton told NZPA the cold snap would not be as damaging as the one that hit last September because lambing was yet to start for most South Island farmers.
Wind chill factor was the most concerning factor for farmers but most were "prepared as they can be", Mr Pemberton said.
Snow has also fallen in many parts of the North Island including in and around Wellington. Many hill roads around the capital were closed this morning, including the Rimutaka Hill Road. The Desert Road and the alternate route through National Park in the central North Island were also closed.
Police were warning drivers to take care on the roads in western Bay Of Plenty with snow falling on the Kaimai Ranges.
And high winds and snow caused trees and branches to tear down power lines cutting power to about 6000 customers across the lower North Island overnight and this morning.
"Supply is being progressively restored to customers and there are currently around 4000 properties without supply, the majority of those being in South Taranaki with a few in rural Wanganui, Manawatu and Wairarapa," Powerco Network operations manager Phil Marsh said.
Mr Marsh said Powerco expected to restore supply to the majority of affected customers by the end of the day.
Snow had settled in Wanganui for the first time since 1974, Constable Simon Beswarick told NZPA.
Auckland ferry services from Birkenhead Wharf and Northcote Point and Rangitoto Island were cancelled this morning due to weather conditions, ferry operator Fullers said.
The MetService is forecasting the heavy snow to continue today and tomorrow.
Snow would fall to low levels in Canterbury, parts of Marlborough, Wellington, Wairarapa, Horowhenua Kapiti Coast, Manawatu, Wanganui, Taihape and Taranaki -- with significant amounts expected to accumulate by midnight tomorrow.
Late Tuesday heavy snow was expected to spread north into Hawke's Bay and the south of Gisborne. Snow was forecast to fall to 400 metres in Auckland.
Strong southerlies and gales around exposed coasts would make the wind feel bitterly cold and create blizzard like conditions in some places.
