A low-pressure system is continuing to bring cold and wet weather to much of the country.
A cold front is now expected to bring "significant snow" to low levels in the south of the South Island overnight and into tomorrow, affecting all alpine passes and closing the Milford Rd.
State Highway 94 in Southland is to close from East Gate (Hollyford) to West Gate (Chasm) from 4.30pm today due to heavy snow forecast overnight.
"Significant snow is also expected throughout Tuesday with the road not expected to reopen," NZ Transport Agency Milford Road advised.
MetService has updated its severe weather information to include a Heavy Snow Warning for Fiordland and a Heavy Snow Watch for inland Southland, Clutha and Central Otago south of about Roxburgh.
There is also a Strong Wind Watch in place for Coastal Clutha and Dunedin.
The forecaster had earlier advised that Dunedin's hill suburbs were included in its forecast for snow tomorrow morning.
"We are expecting snow down to significantly low levels early on Tuesday morning — about 300m in Dunedin and about 200m in parts of Southland and Clutha.
"It is a showery flow, so there will be snow showers for a brief time in the early hours of the morning.
"It will settle, but not for long. We're not expecting large accumulations."
Frost began to roll into Christchurch on Monday as temperatures sat at 1.5C at 8am.
A heavy rain watch is also in place for the Richmond Range including the Rai Valley, Wellington, Horowhenua-Kapiti, the Tararua Range and Taranaki.
Aucklanders should expect a high of 19C on Monday with showers and some heavy thunderstorms followed by a high of 18C on Tuesday, according to Metservice.
Wellington will reach a high of 16C with periods of rain and the possibility of thunderstorms followed by a high of 15C on Tuesday.
Metservice's Ashlee Parkes said the southern regions should also expect bitterly cold strong-to-severe southwest gales tonight, going into tomorrow morning — particularly in coastal areas such as Dunedin.
"It's going to be quite cold first thing, but it should warm up later in the day as the winds ease."
Fellow meteorologist Kyle Lee said snow was expected to fall in inland parts of Otago as well, but not as low as Southland.
He said if snow did fall down to 300m inland, it would affect a lot of roads around the region, especially the higher routes.
"I expect it to cause some form of delays and affect a few higher roads, specifically in the Central Otago region.
"But at this stage it's hard to pinpoint which regions or exactly which roads we think will be affected."
He advised farmers to keep an eye on the forecast to see how it developed, because they might need to move stock to more sheltered areas.
"If they can, they should be prepared to act accordingly to whatever advice is given."
On Thursday, a ridge of high pressure was expected to move on to the country from the Tasman Sea.
- Additional reporting Otago Daily Times