Heavy snow on the roads is likely to cause major disruption to traffic and make driving conditions hazardous, especially about higher mountain roads and passes.
Strong southerlies along with the cold temperatures will make the wind feel bitterly cold.
Farmers are advised that stock may need shelter.
The heaviest snow in Wairarapa, south of Masterton, is expected during Tuesday morning when 10cm could accumulate in 6 hours.
It is expected to be a bitterly cold week, Metservice said, thanks to an Antarctic southerly flow of air spilling across Aotearoa.
This means there will be some frigid days and very chilly nights. Wintry showers are also in the mix, especially for the eastern parts of the North Island.