MetService meteorologist Angus Hines said snow is forecast down to 600m in Fiordland and South Otago.
Tonight and early tomorrow in the far south it could go as low as 300m - similar to the height of Auckland's Sky Tower, which is 328m.
The MetService has issued severe weather warnings - for heavy rain in Fiordland, the Canterbury and Otago headwaters and Westland south of Otira; and for strong winds in parts of central New Zealand and the Canterbury high country and foothills.
The rain warnings, in which thunderstorms are forecast too, are until this evening or early tomorrow morning.
The Canterbury wind warning is until 1am tomorrow and the one for Wellington, Wairarapa, Tararua and parts of Marlborough is until 11am. Both are for severe northwest gales, with gusts reaching 140km/h in exposed places.
"Strong wind gusts could damage trees, powerlines and unsecured structures. Driving may be hazardous, especially for high-sided vehicles," the warning says.
The Transport Agency advised people using State Highway 8 from Twizel to Tekapo to take extra care because of strong winds.
State Highway 94 to Milford was to be closed from the Hollyford Rd junction at 4.30pm because of the forecast snowfall.
The cold fronts causing the rain, snow and wind are expected to weaken as they move on to parts of the North Island north of Wellington and Tararua.
Hines said the North Island - apart from the warning areas - could expect showers, a spell of rain and moderate to strong winds.
Looking ahead to the early part of next week, today's weather pattern is, after a brief respite, set for a rerun on Tuesday, with snowfalls that might descend to an even lower level than in the current weather system.
"We are certainly heading towards winter. Before this week it has been relatively mild for the country."
The forecast
Auckland
Tomorrow
Occasional showers. 19C
Tuesday
Occasional showers, some possibly heavy. 19C
Hamilton
Tomorrow
A few showers. 18C
TuesdayOccasional showers, some possibly heavy. 17C
Tauranga
Tomorrow
Chance of a shower. 19C
Tuesday
A few showers from afternoon. 18C
Wellington
Tomorrow
Rain then fine. Strong northwesterlies. 15C
Tuesday
Isolated showers, rain in the afternoon, possibly heavy in the evening. Northwesterlies, gale in exposed places. 15C
Christchurch
Tomorrow
A few morning showers. 13C
Tuesday
Periods of rain until evening. Northerlies. 16C
Dunedin
Tomorrow
Early showers. 10Cne day apart from early showers. Westerlies.
Tuesday
Showers developing morning, clearing afternoon. 13C