A heavy snow warning is in place for many parts of both islands.
MetService said a rapidly deepening low is moving across central New Zealand overnight, with the heaviest snow expected in North Cantebury and Marlborough above 200 metres, and central and southern parts of the North Island.
State Highway 7 west of Hanmer Springs is closed, and traffic on State Highway 1 south of Kaikoura is slow due to the snow.
MetService said the storm is likely to disrupt travel, and damage trees and powerlines.
Meanwhile, heavy snow has already blanketed parts of the South Island today, affecting many major roads.
As the deepening low moves east, those in the lower North Island could also wake up to snow.
MetService meteorologist Ashlee Parkes said there was a warning for the Tararua and Remutaka ranges overnight.
State Highway 8 from Lake Pukaki to Lake Tekapo in Canterbury has been closed due to snow settling on the road.
A number of road snowfall warnings are in place around the country.
In the South Island, road snowfall warnings have been set for Lewis Pass (SH7), Arthur's Pass (SH73), Porters Pass (SH73), the Dunedin to Waitati Highway (SH1), Crown Range Road and Milford Road.
In the North Island, snow is expected on the Napier Taupo Road (SH5), the Desert Road (SH1) and Remutaka Hill Road (SH2).
In the Wellington region, motorists have been urged to take care on the roads today, with bad weather forecast for this afternoon.
Heavy rain and strong winds are buffeting the capital for the second time in less than a month.
Wellington City Council's chief infrastructure officer Mike Mendonca said they expect surface flooding or slips and people should keep off the roads if possible.
He said contracters were on standby to deal with any weather-related infrastructure problems.
Cook Strait ferries have been cancelled until tomorrow morning due to poor sailing conditions.
Bluebridge and Interislander services will be reviewed late tonight or tomorrow morning.
New Interislander bookings are suspended until Tuesday so that the company can reschedule those who have had their sailings cancelled today.
There is a strong wind warning in place for coastal Marlborough, coastal Wairarapa and Wellington, with severe gale gusts of 120 km/h expected in exposed places.
There is also a strong wind watch issued for Hawke's Bay, Kapiti-Horowhenua and the remainder of Wairarapa including the Tararua district not under warning.
By 2pm Mt Hutt had received 25cm of dry snow over the course of a day.
Ski Time accomodation manager Peter Wood said he woke up to see snow falling in Methven.
He expected snow conditions would be excellent and said he had been getting calls from Queenstown with people keen to come up and ski Mt Hutt after the fresh snow.