Parts of western Scotland will experience strong winds until midnight on Sunday, the Met Office said, while a yellow weather warning for ice is also in place for most of the country 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.
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.”
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, 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.
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.”
Traffic Scotland, meanwhile, have said conditions are likely to be changeable on Sunday, and advice extra time for any essential journeys.