New Zealand Post spokesman Michael Tull said it regretted any inconvenience to customers but the safety of posties and other road users must come first.
There would be no postal deliveries in Dunedin, Queenstown and Alexandra.
Deliveries were being attempted in Cromwell and Wanaka but it may be necessary to halt deliveries, he said.
Latest updates: Wintry weather blast
Areas of Canterbury and Wellington have also been affected by light snowfall and cold southerly winds with hail and sleet on the way, said WeatherWatch.co.nz.
Weather Watch analyst Richard Green said bitterly cold temperatures were hitting Christchurch, which registered its coldest day of the year.
"Temperatures this morning have varied anywhere between minus one to three degrees but throw in that southerly that's blowing fairly breezy in some places, you're looking at minus five degrees. That's what it feels like in the wind if you're stepping outside."
The NZ Transport Agency said the Rimutaka Hill Road between Wellington and Wairarapa was closed due to snow about 9am.
An alternative route for northbound traffic is State Highway 1 via State Highway 57 or southbound State Highway 3 via SH57.
Up to 20 vehicles were reportedly stuck on the road and crews were working to get everyone off the road safely.
Elsewhere in the Wellington region the highways were operating as normal.
The NZTA urged drivers to be cautious and adjust their speeds to suit the conditions.
In Auckland thundery showers and blustery cold winds were forecast for the rest of the day with possible hail, said WeatherWatch head weather analyst Philip Duncan.
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He said there would be a "lull in the torrential showers which are now lining up in the Tasman Sea and marching in towards Auckland".
"The weather will intensify in Auckland this morning and afternoon then ease back this evening."
About 3000 lightning strikes, mostly out in the Tasman Sea and along the western coastline of the North Island, had been recorded today, he said.
The wintry blast was also creating swells of more than eight metres along Auckland's western coastline, which weren't expected to ease until Thursday or Friday.
Warmer, drier weather was expected in Auckland from Wednesday, with highs of 17 or 18 by the weekend, said WeatherWatch.
Chains were still required in most places in the south and motorists were being warned to take extra care particularly over the Lewis, Porters, Arthur's and Lindis Passes.
Snow showers east of Banks Peninsula could move in across Christchurch later today and temperatures have plummeted.
The Milford Road has been closed, as has State Highway 8 between Roxburgh and Alexandra.
State Highway 93 between Clinton and Mataura is also closed.
The Clutha District Council urged motorists to take caution in the snow and treacherous conditions.
Elsewhere, a Port Waikato woman had her roof blown off her home following a possible tornado.
Fire Service Northern Communications shift manager Jaron Phillips said crews were called to the property, on Tuakau Bridge-Port Waikato Road, about 7.20am.
Mr Phillips said fire crews were assisting with tarpaulins after winds blew the roof off the house and shattered windows.
The house is in remote area, Mr Phillips said, and was not aware of any other damage to property in the area.
Mr Phillips said there has been about half a dozen weather related calls this in the upper North Island morning, mainly relating to blown powerlines and alarm activations following a lightning strike in Panmure, Auckland.
Photos: First snow hits South Island
Conditions were expected to clear towards the evening in the South Island but cold conditions were likely to continue for longer in the north.
BRACE YOURSELF: COLDEST DAY TO HIT
Grab your hat, scarf and jacket - Auckland is in for its coldest day of the year today as a wintry blast moves up the country, bringing snow to many parts of the South Island.
MetService said the cold front started "knocking on the door" in Auckland last night - with an expected low of 8C - and would bring cold, showery conditions and strong southwesterly winds today.
Forecaster Leigh Matheson said places exposed to southwesterly winds, such as Manukau Heads, could have gales of up to 110km/h.
The temperature in Auckland was expected to reach just 13C today. However, with the strong southwesterlies Ms Matheson said it would feel more like 10C.
"It's going to seem like a very blustery day."
Conditions would improve tomorrow with the southwesterlies easing off, showers clearing and temperatures rising. The polar blast was also expected to bring widespread snowfalls in the South Island, with temperatures expected to drop to 0C in Christchurch last night.
Snow fell overnight in inland Southland, with falls expected in Otago, inland high country and Fiordland.
Sleety showers may strike Christchurch this afternoon, limiting the day's high to 7C. Wellington would also "cop it a bit" with cold southerlies, sleet, and an overnight temperature of 5C and 8C.
Senior Sergeant Bruce Ross says extreme caution is advised on Dunedin's roads this morning.
"Lookout Point is getting pretty heavy and a lot of cars are stuck up there so people just be very careful getting to work because you're only going to cause problems, crashes and whatever and someone's going to get hurt."
Road snow warnings are in place for Arthurs Pass, Lindis Pass, Porters Pass and the Milford Rd in the south, and the Desert Road and Rimutaka Hill Road in the North Island.
Karena Colle, who owns Valentino's Italian Restaurant in Turangi, said her customers told her snow had started falling on the Desert Road just before 6pm last night.
She hoped it was a sign of a great snow season for the region.
"Let's hope by another month we get the snow fields open. It's good for the fishing when you have a really good cold snap in May and June, gets the trout running up the rivers for fishing. That helps too."
There could be snow in the hill suburbs in Wellington later on today.
MetService forecaster Sarah Garlick says snow is expected above about 500 metres this morning - affecting the very top of the Rimutaka Hill road.
"Expecting that to lower to about 300 metres this evening which also could affect some hill suburbs."
Ms Garlick says it is currently seven degrees at the Wellington Airport - the forecast high today is nine.
Commuters heading over the hill from Wairarapa are being urged to take extra care.
NZTA Wellington operations manager Mark Owen says hopefully the road won't close.
"We've got weather monitoring stuff on the hill so we can predict what's coming and the guys will be out patrolling the road, working with the police and if conditions become too dangerous we may have to look at closing the road."
HIGHS AND LOWS
Whangarei: 14C high, 5C overnight
Auckland: 13C high, 6C overnight
Hamilton: 10C high, 2C overnight
Taupo: 8C high, -2C overnight
Tauranga: 13C high, 3C overnight
Wellington: 8C high, 5C overnight.
- APNZ, NZ Herald and Otago Daily Times
