The worst of the weather is expected to hit Scotland tomorrow while Yorkshire is also set to see more snow over the coming days.
Transport Minister Humza Yousaf said amber warnings for snow and freezing winds along the entire east coast and across the central belt between Edinburgh and Glasgow and as far west as Greenock from the early hours of Wednesday could be changed to red for extreme weather in certain areas.
Forecasters said the worst affected areas could see up to 40cm of snow and a wind chill of -10C.
Amber and yellow snow and ice warnings are in place for Yorkshire with rural communities warned that they could be cut off completely, with power cuts and disruption to mobile phone signals possible.
Mr Yousaf told BBC Radio Scotland: "There is a possibility that the amber warning could be in some areas upgraded to a red. That is a warning for snow that we have never seen since the modern system has come into place in Scotland, that's what the Met Office tell me.
"We are right on the cusp, we are at the strongest possible amber warning, and right on the cusp of potentially becoming a red. That means a high likelihood of a high impact so that could be not just treacherous but frankly dangerous if you travel."
Met Office guidance for red warnings states: "Widespread damage, travel and power disruption and risk to life is likely.
"You must avoid dangerous areas and follow the advice of the emergency services and local authorities."
The worst of the weather so far has been south of the Border where four people have died in car crashes amid heavy snow.
Three were killed in a crash in Lincolnshire and another man died after a collision in Cambridgeshire on Tuesday morning.
Motorists have been warned to take extra care on the roads and drive to the snowy conditions.
Here are the latest reported issues.
Hundreds of schools across the UK were closed on Tuesday.
These are some of the affected areas:
- Wales (223)
- Kent (339)
- East Sussex (62)
- Norfolk (36)
- North Yorkshire (29)
- Lancashire (27)
- West Yorkshire (22)
- Essex (14)
- Surrey (10)
- Aberdeenshire (7)
Three people were killed in a crash in Lincolnshire on Tuesday morning.
The A15 was closed in both directions at Baston after the fatal collision involving a car and a lorry on the A15 in Lincolnshire at 6.15am on Tuesday.
There were 20 collisions within three hours on Lincolnshire's roads, including a school bus with 45 pupils on board, police said.
The children were unharmed after their bus collided with a car and veered off the road near Deeping St James.
A man died and another person suffered life-threatening injuries after three crashes on the A47 in Cambridgeshire.
All the collisions are believed to have involved the same vehicle and saw the road near Peterborough shut in both directions, police said.
Another person was injured and the A120 was partially closed after a 17-car pile-up between Colchester and Elmstead Market, Essex Police said.
Slow-moving traffic caused delays on the M2 in Kent westbound, between junctions seven and five, Highways England said.
HGVs struggling in the snow have caused delays on the M20 in both directions between junctions eight and nine, adding up to two hours to journey times, it added.
The A249 in Kent was closed following a crash between two lorries.
Meanwhile, dozens of stranded motorists had to be pulled from snow drifts on Tuesday morning, the AA added.
Vince Crane, of the AA, said: "With the sub-zero temperatures this week, drivers should allow extra time to properly de-ice the car and check their route before setting off - try to favour gritted roads if possible.
"Accidents happen when people rush so when on the road, leave plenty of space behind the car in front and drive to the conditions."
Several train companies have been hit by cancellations and disruptions and services are expected to be extremely busy.
National Rail Enquiries said severe weather was affecting services on c2c, Greater Anglia, London Overground, South Western Railway, Southeastern, Stansted Express and TfL Rail.
Disruption may continue through Tuesday, Wednesday and Thursday, Network Rail said.
It urged customers to check services before travelling.
London Overground is running a stripped-back service, with between two and four trains per hour on many routes, and no services on other lines, such as between Romford and Upminster.
Train firm c2c is operating a limited timetable and advises its customers not to travel where possible.
Greater Anglia is also running a limited service, with less frequent and slower services between Norwich and Ipswich and cities such as London and Cambridge.
Trains between Norwich and Lowestoft, Felixstowe and Great Yarmouth are cancelled, among others.
Southeastern said it expects to run a normal timetable but if conditions worsen an emergency timetable may be introduced.
British Airways cancelled dozens of flights from Heathrow Airport on Tuesday, while easyJet said it is expecting some disruption.
British Airways said in a statement it was preparing for adverse weather until March 2, saying it was "likely to affect some of our short-haul and domestic flights".
It added: "It is likely at times we will have to proactively cancel some services and re-book customers on to alternative flights.
"Customers on cancelled services can also claim a full refund if they no longer wish to travel.
"We are sorry for the potential disruption to your travel plans and are doing all we can to minimise the effect the poor weather may have on our flights."
North east England and Scotland are expected to see the heaviest snow from Wednesday morning, with 15-25cm likely across Scotland, the Met Office said.