Before the storm arrives, there will be a few showers across most of the country.
"But it will be pretty reasonable compared to what is coming," Dyason said.
The low is forecast to move over the upper South Island tonight from the west, and arrive in the North Island from about midday tomorrow.
Very cold, strong southerlies should spread northwards over the South Island behind this low.
Temperatures are forecast to plummet, with Christchurch reaching just 9C tomorrow and Queenstown 8C and -1C overnight Tuesday.
Snow is expected from Monday night into Tuesday about higher inland parts of the South Island with heavy falls likely. Queenstown and Wanaka could have snow down to lake-level, and places like Naseby were likely to get heavy snow.
Snow is also likely about the higher roads of the North Island later on Tuesday.
There is a heavy snow warning in place for the Canterbury high country to 2pm tomorrow and 6pm in the Kaikoura ranges.
Snow is forecast down to 400m above sea level in Canterbury, with pockets of snow as low as 300m. Over 40cm of snow may fall in areas 700m above sea level.
In the Kaikoura ranges snow is forecast to 400m, and over 40cm may accumulate in areas over 600m.
Road snowfall warnings have been issued for the alpine passes in the South Island, and also for the motorway north of Dunedin out to Waitati.
For Lewis Pass, Arthurs Pass and Porters Pass, snow is forecast above 400m, with the largest accumulations at higher levels.
For the Lindis Pass and Haast Pass as well as the Crown Range Rd and Milford Rd, snow is forecast down to 300m, with the largest accumulations at higher levels.
The Dunedin to Waitati Highway is also expected to see a dusting of snow, with a few cm forecast about the highest parts of the road.
The heaviest snow is forecast to fall tonight, but tomorrow there will still be showery southerlies, with potential for more snow in Otago.
Farmers are being warned to shelter stock and motorists are urged to take great care on southern roads.
MetService meteorologist Claire Flynn said from 9pm rain was expected to turn to snow which may accumulate down to 300m, affecting some hill suburbs in Dunedin.
Federated Farmers Otago president Phill Hunt said the cold snap would be an issue for farmers who had "freshly shorn" stock, and they should be moved to more sheltered paddocks.
He said farmers would be keeping a close eye on the weather, in case it deteriorated further, but for most, the southerly blast was more of a gentle reminder that winter was just around the corner.
"Most farmers won't be particularly concerned about the weather.
"Snow doesn't tend to last long at this time of year."
On Tuesday the front moves over the North Island, bringing strong gusts and heavy rain to most areas.
Strong wind warnings have been issued for most country's western areas.
From 7am to 3pm tomorrow Buller and Westland may get severe southerly gales up to 140km/h in exposed places.
Taranaki, Kapiti Coast, Horowhenua, and the Marlborough Sounds can expect gusts of up to 120km/h from 4pm to 11pm tomorrow.
Similarly strong winds are also forecast for Waikato, Auckland and the Coromandel Peninsula from 7pm tomorrow to 1am Wednesday.
The severe weather will start arriving for most areas in the North Island by midday.
"Places like Auckland could really feel the cold front around midday tomorrow," Dyason said.
Auckland is forecast to plummet from 23C today down to 15C by Wednesday.
In the Central North Island the freezing level will drop to 700m tomorrow, with potential snowfall on the Desert Rd.
On Wednesday the storm will start to ease, but cold southerlies will continue for most.
"It will still be quite miserable in a lot of places," Dyason said.
On Thursday the storm will have mostly moved away from the country, however any relief will be short-lived as another system looks set to arrive Friday.
Today's weather
• Whangarei
A few showers, clearing evening. Westerlies. 24C high, 16C overnight.
• Auckland
Showers turning to rain in the morning, possible heavy falls. Strong westerlies, possible gales. 23C high 16C overnight.
• Hamilton
Fine breaks then a few showers this morning and early afternoon. Rain overnight. Westerlies. 21C high, 14C overnight.
• Tauranga
Fine breaks. A few showers developing in the afternoon. Westerlies. 23C high, 16C overnight.
• New Plymouth
A few showers turning to rain in the evening, heavy overnight. Fresh westerlies. 20C high 15C overnight.
• Napier
Cloud thickening. Westerlies. 24C high, 13C overnight.
• Wellington
Mostly cloudy with the odd shower, turning to rain at night. Southerlies turning northeast in the evening. 17C high, 8C overnight.
• Nelson
Overcast, and rain at night with heavy falls. Northerlies developing evening. 19C high, 8C overnight.
• Christchurch
Overcast with a few light showers, then rain at night. Southeasterlies. 13C high, 4C overnight.
• Dunedin
Cloudy. A few showers from evening. Southwesterly picking up. 11C high, 5C overnight.
