After a weekend of freezing temperatures across most of the country, a big high is in the forecast, bringing fine weather in the new week.

The outlook for Monday according to MetService will be mainly fine around the country, aside from scattered showers in western areas.

Sunshine is on the cards all the way from Auckland to Fiordland and along the Southland coast - but that would mean drought-stricken Auckland will be missing out on the much-needed rain.

There has been slow improvements for Auckland's water storage, with storage levels for the region's dams now at 45.1 per cent.

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This has gradually increased since Queen's Birthday weekend, when the levels sat at 43.3 per cent.

Snow on Mt Dobson near Tekapo on Sunday. Photo / Supplied
Snow on Mt Dobson near Tekapo on Sunday. Photo / Supplied

Watercare CEO Raveen Jaduram said Aucklanders are playing their part - because demand for water has decreased.

Jaduram said the region is already ahead of its targets for June and the small amounts of rain and decreased demand have made a difference.

Aucklanders are being urged to keep their water usage under control, even as the country is expected to move to alert level 1.

Jaduram said level 1 may have some impact, with more businesses getting back on track and through commercial activities.

A cold front that moved up the South Island on Sunday brought freezing temperatures down South.

Tekapo was the coldest place where people woke up to a freezing -6.6 C, followed by Pukaki Airport at -5.9C and Alexandra at -4.8C.

The temperature at Christchurch Airport at -3.3C, and snow was down to between 800m and 900m for Fiordland, Southland and Clutha on Sunday evening.

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MetService meteorologist Andy Best said however that the temperatures were normal for this time of the year, with only Christchurch and Kaikoura about three to four degrees lower than usual.

Philp Duncan of WeatherWatch said New Zealand is in for a cooler southwesterly flow for most of the week because of a massive high-pressure system.

"Next week leans drier than average in many places with showers here and there and cooler West to Southwest winds will be colder the further south you go," he said.

"Next weekend the high should cross New Zealand, bringing lighter winds and a newly forming easterly flow for northerners."

According to MetService, from Auckland southwards, there will be cloudy periods and isolated showers becoming more frequent from the morning and then easing later on Monday.

It will be fine and frosty for Nelson, Marlborough and Canterbury in the morning and night, and showers with possible hail from Buller to Fiordland, also coastal Southland and Clutha.

Fine weather, with just isolated showers is in the forecast for most of the country from Tuesday to Thursday.

Rain with develop south of Taihape and Gisborne on Friday, but the weather will remain fine further north. The South Island can expect morning rain, the North easing to isolated showers.