Severe weather watches have been issued for the upper North Island with heavy rain and gales forecast tipped for the beginning of the week.
There are also snowfall warnings for a number of roads around the country.
The MetService warned of strong wind in Taranaki, while heavy rain warnings are in place for Northland and the ranges about Gisborne.
Civil Defence urged Aucklanders to stay updated with forecasts, with strong wind and heavy rain watches in place for the city.
Eastern parts of Auckland north of the Harbour Bridge, Great Barrier Island and the Coromandel Peninsula are included in the heavy rain watch.
Winds could turn to gales in exposed places, with wind warnings in place for Auckland until Tuesday morning.
Twenty to 30mm of rain had fallen across Auckland in the 24 hours to Monday afternoon, according to MetService meteorologist John Law.
Another 10mm was expected for the afternoon. While rain cleared briefly yesterday morning, Aucklanders are waking to more wet and windy weather on Tuesday morning, although this should clear around sunrise.
Kerikeri has already had 40mm of rainfall over the last 24 hours, with 38mm falling in Kaitaia.
In Northland, the MetService predicted 50 to 70mm of rain, with a warning lasting until 3pm.
It could cause slips and flooding in the northern and eastern parts of the region.
Law said, "normally we think about issuing a rainfall warning for above 100mm of rain in 24 hours, but because this is on top of what we've already seen, we've slightly lowered our criteria because it's already sodden and it could cause slips and flooding".
Snowfall warnings for the Ruapehu area have been issued by MetService, with more than 30mm of snowfall forecast for Monday night.
MetService meteorologist, Dan Corrigan, said a road snowfall warning will be in place from 3pm Monday until 3am Tuesday, during which he expected 25-35mm of snow to fall on roads.
Corrigan said a heavy snowfall will be in place from 5pm Monday to 5am Tuesday.
Corrigan said both warnings were the result of the same low-pressure weather system crossing the upper North Island.
"What that's doing is at upper levels in the atmosphere it's pulling down moisture from the tropics, which is how to get good heavy precipitation, and underneath there's cold and a southeasterly flow undercutting that, which is really allowing the snow to penetrate to low levels."
He said due to this same weather system, some snowfall was expected for the hill country of Whanganui as well.
While Whanganui would not see snowfall, Corrigan did expect a steep drop in overnight temperatures in the city for the week.
He expected overnight temperatures to drop as low as 2-3 degrees overnight, with ground frost particularly likely in Whanganui on Wednesday morning.
However, the low-pressure system causing the snowfall on Sunday night was expected to move on to the east of the country relatively quickly, meaning days of the week were expected to be full of sunshine, with southerly winds throughout.
Due to this, after a high temperature of 12 degrees on Tuesday, daytime highs of around 14-16 were expected across the week.
Snow fell in Dunedin and around Otago as a wintry blast moved up the South Island.
There were reports of snow in Dunedin's hill suburbs, and there were flurries in the central city around midday on Monday.
Snow also dusted many hill areas in inland Otago.
A MetService spokesman said a cold wintry blast was spreading up the South Island and the next few days would feel like a return to winter, even though it was technically spring.
"I'm hoping people haven't put their winter woollies away yet," the spokesman said.
An updated MetService forecast on Monday morning said a road snowfall warning for Dunedin's Northern Motorway (State Highway 1) would be in place until 9pm, with snow showers forecast for summits overnight and lowering to about 100m today, with 1cm to 2cm of snow accumulating in places.
Motorists were yesterday warned roads would be treacherous today, following a spate of incidents caused by blustery weather which tied up emergency services in the South yesterday.
Yesterday's expected high was about 6C, when usually at this time of year it would be about 13C, the MetService spokesman said.
On Tuesday, Dunedin could expect a high of about 8C while temperatures across most of the South Island remained in single digits.
Mosgiel could be in for a frosty morning, he said.
A high of 12C was forecast for Wednesday and the rest of the week would likely stay in double digits, he said.
The potentially hazardous road conditions follow on from a day of high winds which battered the South on Sunday.
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