The Met Office has issued a yellow ice warning for Staffordshire but said temperatures should rise slightly through Tuesday.
Several inches of snow fell during Sunday and a yellow "be aware" ice warning is now in place for the Eastern region.
The Met Office later issued a severe snow and ice warning for Grampian, the Highlands, Orkney and Shetland, Angus, East Lothian and the Borders.
The Met Office has issued a yellow warning of ice for the region for Tuesday.
They are also warning of ice affecting East Anglia, southern England and south Wales.
More snow is possible overnight, especially in the east of the county, and the Met Office is warning of ice on untreated surfaces.
The Met Office has issued a yellow "be aware" warning of ice for a large chunk of the UK from London in the south east, across north Wales up to Northern Ireland and across northern England and southern Scotland.
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"The Met Office is warning of widespread ice this morning, " said BBC Wales weather presenter Sue Charles.
In case of the latter, pack an emergency kit for the trunk that, at the least, contains jumper cables, a flashlight, ice scraper, flares or warning triangles, extra gloves and hats, blankets, snacks, a first aid kit and a small snow shovel and a bag of sand or cat litter to help should your car get stuck in the snow.
The Met Office has issued a yellow warning of snow and ice for the West Midlands, advising traffic conditions may be difficult and dangerous.
The office has also issued a yellow warning of snow and ice for most of the UK and advised traffic conditions may be difficult and dangerous.
The Met Office has issued an amber snow warning for mid, north and east Devon, and a yellow warning for snow and ice for the whole county.
The Met Office was warning of a risk of ice after temperatures dropped to -6C (21F) overnight.
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