Parts of England have seen some light snow overnight, as forecasters warn a second, heavier, band will fall across large areas of the UK in the afternoon.
The Met Office has issued an amber "be prepared" warning for snow disruption in north-east England, Yorkshire and Humber, and the East Midlands.
The heaviest overnight snowfall was 3cm in Nottingham and across the Pennines.
Parts of Scotland, which already experienced snowy scenes on Sunday, can expect to see more snow on Monday.
It marks the start of what forecasters are predicting will be a bitterly cold week.
Temperatures are expected to drop to around -10C across rural Scotland on Monday night and possibly as low as -4C or minus -5C across other parts of northern and eastern England.
During Sunday, snow fell in many parts of northern and central England, as well as in Wales - and there were warnings that this could cause travel disruption early on Monday in those places where it had fallen on untreated surfaces.
There was also snow late on Sunday into Monday in north-east England, eastern England and Kent.
Leeds Bradford Airport said adverse weather conditions was disrupting some flights.
One of the last places to see snow was London, where it began falling after 05:00 GMT.
Northern and eastern regions of England are expected to have the highest snow accumulations, the Met Office warned.
Wales and south-east England are also expected to see some snow during Monday, with the far south-west of England and Northern Ireland being the only regions untouched by the severe cold.
BBC forecaster Steve Cleaton said there could be some travel disruption for those in eastern parts later: "I think particularly around Nottingham. It looks like it's going to be more of a problem this afternoon and into this evening, " he said.
The three Met Office amber warnings were issued about 16:00 GMT on Sunday, having been upgraded from yellow warnings advising people to "be aware" of severe weather. They cover from 09:00 GMT to 23:00 GMT on Monday.
The Met Office said the severe cold weather and icy conditions could "increase the health risks to vulnerable patients and disrupt the delivery of services."
It issued its "cold weather action" alert level, activated when average temperatures of -2C occur for 48 hours or longer, or there is heavy snow and/or widespread ice.
The cold spell is being caused by an abrupt jump in temperatures high in the stratosphere, which can bring snow, forecasters explained.
It is set to continue throughout Tuesday and Wednesday, with snow forecast for eastern England and Scotland on those days.
Councils in Scotland have more salt in stock or on order than ever before to cope with the risk of snow and widespread ice, Scotland's transport minister said.
Strengthening winds later in the week will make it feeler colder, the Met Office said.