Strong winds are expected to hit parts of western Scotland and Northern Ireland’s east coast between 4am and midnight on Sunday, the Met Office said.
A yellow weather warning for ice is also in place for most of Scotland, northern England and the Midlands until 9pm.
Freezing rain and “treacherous ice” is expected to occur in those areas, leading to possible disruption, the warning said.
Met Office forecaster Luke Miall said Sunday will not be “particularly pleasant” for most people, with winds reaching up to 40mph inland across England.
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He said: “It’s going to be a bitterly cold day. Certainly where you’ve got freezing rain and ice, combined with those strong winds.”
Overnight temperatures on Saturday are forecast to drop to minus 8C in Scotland and between minus 1C and minus 5C in England and Wales.
Daytime temperatures will hover around 2C in eastern areas, increasing to 11C in south-west England.
A yellow weather alert for wind warns of gusts of up to 80mph and large waves for coastal areas in western Scotland and Northern Ireland’s east coast.
Temperatures will begin to increase from Monday, with the mercury rising to 13C across England.
However, Mr Miall said the weather will be “quite wet and windy” for most of the week.
He said: “We will be hovering between 7C to 12C, I suspect, through Tuesday, Wednesday Thursday.
“Most of the snow will start melting early in the week, with the exception being Scotland because they have had so much of it.”
The coldest UK temperature for 65 years was recorded at Braemar in Aberdeenshire on Wednesday night, when the mercury dropped down to minus 23C.
A record low temperature for February was also recorded in England and Wales when temperatures in Ravensworth, North Yorkshire, dropped to minus 15.3C overnight on Thursday.
The chilly conditions froze Trafalgar Square’s fountains and brought large amounts of snowfall to regions across the country.
In Derbyshire’s High Peak area, the impressive Kinder Downfall also froze, turning the 98ft waterfall into a slippery climbing wall.
Public Health England (PHE) has extended its cold weather alert through the weekend and has urged people to check on vulnerable relatives and neighbours.
Dr Owen Landeg, group leader for extreme events and health protection at PHE, said: “Cold weather can have a serious impact on health, particularly for older people and those with heart and lung problems, as it increases the risks of heart attacks, strokes and chest infections.
“Make a call, or socially-distanced doorstep visit if they live close by, to remind them to heat their home to at least 18C, 64.4F, and to keep up to date with the forecast.
“It’s also helpful to check they have enough food and drinks and any medicines they need.”