"Wind chill may be the main problem for many southern farmers, with livestock exposed to sub-zero daytime temperatures in the wind around Southland and Otago and potentially Canterbury's high country."
The snow won't be restricted to the South Island.
Waiouru, the Desert Rd, Ohakune and National Park are also expected to receive snow.
The central North Island town of Taihape is also listed as a "borderline" snowfall location.
Areas that won't be affected by snow are also expected to register some chilly temperatures early next week.
"Both islands are impacted by the cold, starting Monday in Southland and peaking in Northland by Wednesday morning," WeatherWatch's forecast states.
Temperatures in the central North Island could drop to -6C on Tuesday night.
According to the MetService, rain is forecast for the Auckland region on Sunday, before the week becomes fine, but temperatures remain chilly.
Overnight temperatures could drop to as low as 4C.
The pending cooler temperatures come as New Zealand is expected to record its warmest June on record.
Niwa meteorologist Ben Noll told the Herald earlier in the week the past few weeks had been substantially warmer than average across the country.
That had been prompted by warm sea temperatures in the western Pacific fuelling northerly low-pressure systems, bringing warm air to New Zealand.
Up until June 20 the nationwide average temperature was 10.97C, well above the long-term average of 8.59C.
"If the month ended today, it would become the country's warmest June on record, according to Niwa's seven-station series," Noll said.
The highest temperature was 22C at Leigh on June 19.
There are more than 80 locations tracking toward a record or near-record warm month.
Niwa also said a surge of freezing air from the Southern Ocean could approach the country from next Monday or Tuesday, bringing a chance of snow to low levels and icy, strong southerly winds.
A return to milder conditions is possible during the first week of July.
