The whole county will see daytime temperatures of only one or two degrees, with nighttime levels below zero through the weekend and beyond.
Sleet and snow is also likely in places.
The weekend itself will see a frosty start with ice on untreated surfaces. The days will remain cold with sunny spells and scattered snow showers, mainly towards the coast.
Yesterday the county was placed under a “level 3 cold weather alert”, triggered issued when severe weather is occurring, when average temperatures have dropped to 2°C or below, and when widespread ice and heavy snow is present, was in force across the region.
Dr Mike Gent, consultant in communicable disease control at Public Health England Yorkshire, said: “The Met Office says that many places are going to feel really cold for the next few days, which may be a bit of a shock after our recent milder weather, so it’s really important people take extra care when out and about.”
There was also a warning from Andrew Proctor, director of advice and support at Asthma UK, who said: “With very cold weather expected across much of the UK this week, particularly on Thursday, people with asthma need to take extra care.
“Cold air can have a severe impact on people with asthma. As many as three-quarters of people with asthma tell us it can trigger symptoms, making sensitive airways tighten up quickly and putting people at risk of a potentially life-threatening asthma attack.
“If you find cold weather makes your asthma worse, make sure you wrap up warm, carry your reliever inhaler, and know what to do if your symptoms get worse.”
The cold weather comes as Yorkshire continues its recovery from the damaging floods of the Christmas period.
Environment Agency flood warnings remain in place in North Yorkshire for the rivers Derwent and Ouse at Old Malton, Stamford Bridge and York.