Yellow warnings have been issued by the Met Office across the south and east of England, Wales, Northern Ireland and Scotland.
Forecasters say there could be some impact on power supplies and mobile phone signal as temperatures fall as low as -6C.
They have also warned of a danger of vehicles being stranded, longer journey times on public transport, and icy pavements leading to slips and falls.
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Parts of Scotland could see the mercury fall as low as -6C (21F), the Met Office said.
The southwest, Wales and the southern Midlands into the southeast were warned to prepare for ice overnight, with temperatures down to -3C (27F).
The northwest, much of Scotland and Northern Ireland were told to expect equally cold temperatures and widespread snow showers.
And an icy wind chill will leave many parts of the UK feeling several degrees colder than it actually is.
Sky weather presenter Joanna Edwards said: "Temperatures dropped as low as -4C overnight, with a widespread frost for most.
"While these may be a wintry mix, the greater problem is likely to be that of the showers falling on sub-zero temperatures causing instant ice."
The Met Office said: "Heavy hail and snow showers are expected during Monday morning and will lead to ice and snow accumulating on many surfaces.
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"The showers will be heaviest and most frequent across parts of western and northern Scotland. Longer journey times by road, bus and train services are likely while some vehicles could become stranded.
"Ice is likely to form on untreated pavements, cycle paths and roads leading to some injuries from slips and falls. Power cuts may occur and other services, such as mobile phones, may be affected."
Snow showers caused disruption on the roads on Sunday, with North West Motorway Police tweeting there were "numerous reports" of accidents on the roads due to the conditions, and urged drivers to slow down.
Milder temperatures are set to return mid-week.