Those in the South Island would feel a drop in temperatures, with showers also forecast around the southern and western parts of the island, MetService said.
A brief respite in the cold weather on Sunday was possible, with clear skies expected before another burst of cold air across the country.
Icy temperatures were also likely to bring significant snowfalls for the Southern Alps and snow showers for parts of Southland, Otago and Westland to low levels on Sunday.
For North Islanders, rain was expected on Saturday.
WeatherWatch said a "sizeable storm" in the southern ocean was likely to push gales and rain into southern parts of both islands this weekend.
The low would churn south of New Zealand until next week, with the coldest of the weather moving northwards on Sunday and Monday.
"Invercargill will go from highs around 12 or 13 to highs of 7 and 8 this coming Sunday and Monday," WeatherWatch forecaster Philip Duncan said.
"The wind chill factor will certainly feel below zero in exposed places."
Northern centres like Hamilton, Auckland, Whangarei and Tauranga were unlikely to have such a dramatic drop in the mercury, with highs expected to slide by a degree or two by Monday and Tuesday, WeatherWatch said.
Frost and fog was possible on Tuesday and Wednesday in those areas.
Those in the South Island would likely see a lift in temperatures by Wednesday.
Watch WeatherWatch report:
Heavy rain warnings:
* Fiordland, north of Doubtful Sound, now until 10am Friday
* Ranges of Westland, south of Otira, 3pm until 5pm Friday
* Headwaters of Otago lakes and rivers, now until midday Friday
* Headwaters of Canterbury lakes and rivers, now until 5pm Friday
* Ranges of Buller and Westland, north of Otira, 9pm today to 9am Saturday
*
Strong wind warnings
* Canterbury, especially inland North Canterbury, Friday
* Marlborough, Friday afternoon to Saturday morning
* Wellington, Friday afternoon to Saturday afternoon
* Wairarapa, Friday afternoon to Saturday evening
Source: MetService
