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In a severe weather outlook, MetService says the front is expected to deliver a cold and showery south to southwest flow across the country.
Snow was expected to lower to 200m to 300m over the South Island on Monday and possibly as low as 500m to 600m across the lower and central North Island on Tuesday
"Snow is expected to affect many higher roads and farms in these areas, and there is a moderate risk of snow accumulations reaching warning criteria about inland Canterbury and Kaikoura from Monday evening to early Tuesday morning."
As the low deepened east of the South Island on Tuesday, southwesterlies were expected to strengthen and there was a low risk of severe gale southwest winds about coastal Canterbury from Banks Peninsula northwards, the Kaikoura Coast and southern Wairarapa.
Late Tuesday, another front was forecast to approach the far south of New Zealand, and the west to southwest flow ahead of this front should strengthen.
The MetService said it had "moderate confidence" of west to southwest gales becoming severe about the south coast of the South Island including Stewart Island, while the confidence was low for northern Wairarapa including the Tararua District, and central Hawkes Bay from later Tuesday and during Wednesday.
Temperatures are set to plummet on Monday.
Dunedin, Oamaru, Gore and Invercargill are all predicted to reach only 8degC, while Queenstown and Alexandra are forecast to reach 9degC.