The coldest night of the winter hit the UK on Monday after temperatures plunged in Scotland.
The Met Office recorded minus 12C (10.4F) at Kinbrace in Sutherland - the coldest measurement of the winter so far.
In England, the temperature hit minus 8.2C (17.2F) in Benson, Oxfordshire, and even as far south as Odiham, Hampshire, minus 6.5C (20.3F) was recorded.
Sleet and light snow on high ground in Scotland are likely, along with a few wintry showers expected for northern parts.
Skies are expected to clear on Tuesday evening from the south where gardeners were warned of a hard frost, while freezing fog could affect travel.
More weather warnings are expected to be put in place on Tuesday night in preparation for more ice and fog on Wednesday morning.
Towards the end of the week, temperatures are expected to warm up slightly as less cold air edges in, bringing rain with it.
Met Office forecaster Lindsay Mears said: “People should be aware that wet surfaces and existing snowfall on the ground will turn to ice in most places overnight.
“There is a yellow weather warning across parts of Scotland as temperatures drop.”
The warning covers large sections of southern Scotland. It also issued snow warnings for the Strathclyde and the central, Tayside and Fife area.
Mountainous areas saw temperatures plummet to below -10C.
Glasgow dropped to -5C, with Aberdeen at -3C, Edinburgh at -2C and Inverness -1C.
The forecast for tonight with see patchy drizzle along western fringes of Scotland. Elsewhere, a dry and fairly chilly night for many.
Mist and fog patches may form in prone areas but likely to be cold where skies become clear, meaning a local frost may form.
A locally frosty start tomorrow with areas of fog slow to lift, especially in northern Scotland where it may linger all day.
Otherwise, it will be a dry day with bright or sunny spells developing. Light winds. A chilly day again, especially in the north of the UK.
The outlook for the rest of the week will see it dry in eastern areas on Thursday with sunny spells, but turning cloudy in western areas with the odd spot of rain or drizzle.
Rain will push across the country on Friday and will be followed by scattered showers that will affect mainly northern areas.
Lindsay Mears added: “The week ahead will continue to be cold and frosty, with temperatures falling below zero.
“We are currently getting Scandinavian conditions, but towards the end of the week it will get milder. An Atlantic low coming in from the west will bring in milder air and temperatures will rise, providing a respite from the very cold weather.”