The winds would target the South Island late this afternoon until tomorrow morning before reaching the North Island from tomorrow afternoon.
Flynn said temperatures would start to warm up before the front hit the South Island today and reached the North Island on Wednesday night.
"The following night [in the South Island] it is looking like it could be getting frosty again since that front has then gone through and we've got colder in the South Island again and southwesterly winds."
The North Island - particularly inland areas - could be frosty overnight but will warm up before the front crosses the North Island, according to MetService. Another cold snap would hit the North Island overnight on Thursday.
"Overnight tomorrow night won't be so cold for the North Island, but after that things will start to cool off again and we will get some cooler temperatures by the end of the week again."
It would be mostly fine all over for the weekend, with showers hanging around the east and south coasts on Friday and most areas clear by Saturday.
Weather Watch head weather analyst Philip Duncan said it was now tracking the second cold snap which moved up the South Island over Wednesday and across all of New Zealand by the end of Thursday.
"Thursday on the other hand is a very different story. Temperatures take another beating across the country."
However, although Thursday night would be cold again in most places, the east coast and southern areas of both islands would the most exposed to the next windy cold snap, Duncan said.
"By the time the weekend arrives a high should be coming in, perhaps locking in frosts but also calm weather and milder afternoons."