Temperatures are set to fall as low as -10C, with snow forecast for London, the South East and Scotland and yellow warnings for ice in place for much of the rest of the UK.
A yellow warning for snow is in place over much of Kent and Sussex tomorrow morning.
There is also a yellow warning for ice with wintry showers expected across Northern Ireland, Wales and northern England as temperatures fall.
The cold snap comes after widespread flooding left big parts of the country submerged in the past week.
The Met Office issued a lengthy warning for snow and ice for northern Scotland from Sunday to Wednesday.
"A few centimetres of snow are likely at low levels over a given 24-hour period, with the potential for 10-15cm above 200 metres, especially across parts of the Highlands," it said.
"Ice will be an additional hazard, especially Tuesday night."
Residents have been urged to be careful of icy patches on untreated roads, pavements and cycle paths, and longer journey times by road, bus and train services are likely.
The yellow warning for Kent and Sussex is in place between 2am and 8am on Monday morning.
"There is a chance that heavy rain will turn to snow in places, which may cause some travel disruption on Monday morning," the warning said.
"There is a small chance of travel delays on roads with some stranded vehicles and passengers, along with delayed or cancelled rail and air travel."
The forecaster added: "By Sunday most of the UK will be in the northerly airflow, with lower temperatures spreading further south overnight.
"Showers will fall increasingly as sleet and snow in the north, even to lower levels. Some showers further South and West, and perhaps a more persistent spell of rain overnight into Monday, could also turn to sleet and snow mainly over high ground such as the Brecon Beacons, Exmoor and Dartmoor.
"Overnight frost will become more widespread by Monday night, with overnight temperatures below 0°C across much of the UK. Temperatures could get down to -10°C in sheltered glens, or across high ground areas of Scotland where there is lying snow."
In addition to the nosediving temperatures, more than 100 flood warnings are in place across the UK.
The Environment Agency had issued 119 flood warnings and 192 flood alerts in England as of early Sunday morning, up from 98 warnings and 169 alerts on Saturday.
Earlier, flood defences, including boarding, were deployed in York city centre.
City of York Council said it had taken the measure to keep the area "safe and open" as it urged visitors to plan their journeys in advance.
Rescue workers used a boat to navigate the floodwater in the centre of York after the River Ouse burst its banks.