An active trough of low pressure is moving eastwards across the country, bringing heavy rain to the lower North Island and strong winds to the east of that island.
Meanwhile, heavy snow is possible for inland parts of mid and northern Canterbury and Marlborough on Sunday.
Monday sees a rush of cold air down south, bringing snow to Southland and Otago throughout the day. The snow is expected to be heavier above 400 metres, but a few flakes could make it to sea level, the forecaster says.
Snow showers were set to affect Dunedin's Northern Motorway (State Highway 1, Dunedin to Waitati) for most of Monday from 10am until midnight.
A heavy snow watch remains in place for Central Otago south of Lake Wakatipu and Roxburgh, Clutha, Southland and Fiordland, south of George Sound from 2am until 5pm.
There would be frequent showers and strong southwesterlies, with snow to low levels.
"Expect heavy snow at times above 400 metres, where snowfall may approach warning criteria in places."
Snow showers were also forecast for the Crown Range Road, linking Queenstown and Wānaka, the Milford Road (SH94) in Southland, and the Lindis Pass (SH8) in Central Otago throughout Monday.
But the cold snap would first be felt in Canterbury on Sunday, where a heavy snow watch was also in place for inland parts of Canterbury, north of Waipara and Marlborough, south of State Highway 63 from 10am until 10pm.
Rain turning to snow has been forecast for Canterbury alpine highways Porters, Arthur's, Lewis and Lindis throughout the day.
In the North Island, snow showers were forecast for the Desert Road (SH1) and the Remutaka Hill Road (SH2), linking Wellington and Waiarapa, from early on Monday.
State Highways affected
South Island
Arthurs Pass (SH73)
Milford Road (SH94)
North Island
Remutaka Hill Road (SH2)
From 1am until 6am on Monday
Some snow flurries may affect the summit overnight but little if any snow is expected to settle on the road.
Desert Road (SH1)
From 7am until 10pm on Monday
Snow showers are expected above about 1000 metres throughout the day where 1cm to 2cm of snow may accumulate at times.