More than 100 schools have been closed in Scotland, and dozens have also shut in Merseyside.
A cold spell fuelled by wintry Arctic air is set to continue throughout Tuesday and into the week ahead.
Met Office yellow warnings for snow and ice are in place for Scotland, Northern Ireland, much of northern England and north Wales throughout the day.
Temperatures fell below freezing across the UK overnight as biting winds continued to blow in from the north.
Travel disruption is likely, especially in north-west England and Scotland.
National Highways issued a severe weather alert for the North West and warned freezing temperatures and snow were expected to make roads dangerous from 05:00 GMT on Tuesday.
Scotland will see the worst of the weather, with up to 20cm of snow forecast across higher ground and enough to create travel disruption in areas further south.
On Monday, Transport Scotland warned motorists to expect “severe impacts” from snow and ice on the roads.
National Rail has warned there could be disruption across the network throughout the week.
The Met Office has said temperatures so far this week are around 5C to 6C lower than usual for this time of year.
A yellow snow and ice warning covers Northern Ireland until 11:00 GMT on Tuesday, and lasts throughout the day for Scotland, parts of north Wales, Northumberland, and northern England west of the Pennines.
Northern Ireland and parts of northern England are also forecast to see some snow, but rain and sleet is likely to mix in at low levels, with heavier snowfall expected to be confined to hills.
Ice will be a further hazard across the UK, with temperatures struggling to rise far above freezing during the day, although highs of 6C will be seen in southern England and southern Wales.
More snow is expected in parts of Scotland, Northern Ireland, northern England and north Wales on Tuesday night.
While conditions will be bright and dry elsewhere, temperatures will feel below zero for most due to icy winds.
The UK Health Security Agency has issued an amber Cold-Health Alert for the whole of England, meaning it expects the NHS to see increased demand, particularly from – but not limited to – older and vulnerable people.
The cold spell has resulted in automatic £25 payments for households in receipt of certain benefits being triggered in more than 220 postcodes where temperatures are expected to be below zero for a full week.
The assistance with heating costs for eligible households applies in some parts of Wales and northern and eastern England.
Looking ahead to the rest of the week, BBC Weather forecaster Ben Rich said: “An area of low pressure will move across France on Wednesday and may graze the south of England. It looks most likely that any amounts of snow here will be small and confined to coastal counties.
“However, computer models have struggled with this aspect of the forecast, so it’s worth keeping up to date as we firm up on the details.
“Milder weather – along with some wind and rain – is expected to sweep across the UK over the weekend bringing the cold spell to an end.”
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