The Met Office issued a yellow warning for ice, which is in force until 10am GMT, following freezing temperatures on Sunday evening and overnight.
Forecasters have warned of up to 5cm of snow on higher ground and sprinklings of snow predicted on lower ground.
A WXCHARTS snow depth weather map shows how total snow accumulation builds up from Monday to Friday, this week.
Scotland is expected to feel the brunt of UK snowfall, however, sprinklings are expected to be felt down toward the northwest and Midlands.
Another weather map from Weather Outlook suggests Scotland and parts of the northwest will get a dusting of snow today at midday, moving slightly further south before clearing altogether by 9pm.
The entire UK could be covered in snow at midday on Tuesday, with heavy levels indicated to fall on the western coast of Scotland at around 6am.
The Met Office has warned of disruption to half term holidays as most of the country will see a mixture of wind, rain, sleet and snow over the coming days.
Met Office forecaster Helen Roberts said: “There will be strong winds across much of the country on Monday with the risk of showers which will be wintry in parts.
“A squally system comes in on Tuesday bringing heavier bursts of rain and some more strong winds, there will be a further risk of snow especially across the northern half of the country.
“It is a similar picture on Wednesday with more heavy showers, we could see 40 to 50mm of rain over high ground in Wales and the southwest; there will be further gales and strong winds which could reach inland.
“By the end of the week, we are back into a colder Polar maritime airmass bringing a further mix of wintry showers.”
BBC Weather warned the UK would face further frozen conditions with “significant” snow and ice expected after a chilly weekend.
BBC Weather forecaster Nick Miller said: “A frosty start across the United Kingdom this morning. Icy in places too. Wales and North West England, Northern Ireland into Northern and Western Scotland.
“There have been some snow showers around overnight giving a fresh covering in places here and there will be a few more to come as we go through this morning.
“So perhaps some difficult travelling conditions in some spots here.”
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