The Met Office acted quickly to issue a severe weather warning for snow and ice in Scotland and along England's east coast.
In Wales, 71 schools were forced to close in Flintshire, 11 in Wrexham and 49 in Denbighshire.
Motorists are being warned of "Black Ice Monday" - a combination of sub zero temperatures, snow, rain and sleet will form to create unsafe invisible ice on the roads.
"Some roads and railways are likely to be affected with some journey times taking longer".
"Some injuries are possible from slips and falls on icy surfaces and there will probably be some icy patches on untreated roads and cycle paths".
A low of -13C (9F) was recorded on Monday night in Shawbury, Shropshire - the coldest night of the year so far.
The Met Office added: "A spell of heavy snow is likely over parts of Wales, the Midlands and parts of Northern and Eastern England on Sunday".
AA president Edmund King said: "We expect Tuesday to be extremely busy as temperatures plummet overnight, causing even more hazardous conditions on already wet and slippery roads".
Birmingham City Council had to cancel all council-run school transport services on Monday as the cold snap continued.
Western Power Distribution said 99,500 customers were cut off on Sunday across the East Midlands, South Wales and the South West. It is predicted that most areas within North West England will struggle to beat temperatures of freezing.
Thousands of homes have been left without power after being hit by the weather.
It said no rail operators have announced changes to their planned Sunday services, but to check before travel.
Chiltern Railways, Arriva Trains Wales and Greater Anglia were reporting major delays on Tuesday morning.
Airports have also been affected across the United Kingdom, with Heathrow warning of delays to more flights on Monday after crews and aircraft were left "out of position".
P&O ferries are delayed by up to three hours because of the weather.
By Monday afternoon, about 9,000 homes were still without power, including more than 6,700 in the West Midlands. Travellers are being told to check in and will be put on the first available sailing.