Strong winds with gusts of 70mph will batter northern parts of England, and higher ground in Scotland could be blanketed in up to 5cm (2in) of snow.
Motorists are being warned that snow and rain overnight may turn to ice on roads as clear conditions bring freezing temperatures.
The Met Office has issued severe weather warnings for most of Scotland and northern England for wind and ice.
It said on Tuesday: “The north or northwesterly winds will increase during the early hours of Wednesday, with gusts perhaps reaching 60-70 mph in places.
“The public should be aware that the winds are likely to be strong enough to cause some local disruption to travel, and possibly some minor damage to buildings and trees.”
Alexi Boothman, a forecaster with MeteoGroup, the weather division of the Press Association, said temperatures were markedly lower than the average for this time of year.
Maximum temperatures in England and Wales were around 6C (42.8F) or 7C (44.6F) on Tuesday, below the average of 10C (50F) or 11C (51.8F) .
Large parts of England will see temperatures reach minus 3C (26.6F) or minus 4C (24.8F) on Wednesday, caused by cold winds from the North.
But while wintry conditions bring cold weather, only Scotland is likely to see any substantial settling snow.
Ms Boothman said: “There is potential for getting quite a lot of snow where the ski resorts are, but generally we are looking at wintry showers rather than heavy snow coming through.
“On high ground and mountains and hills like the Cairngorms we are looking at the potential for 3-4cm, (1.25in to 1.5in) possibly even 5cm (2in) of snow.
“There will be really quite strong winds in the North, with wintry showers across central and northern England, turning into rain.
“We are looking at wintry, breezy conditions that are not very nice, but snow is unlikely to settle in England, and conditions by the end of the week will be drier with lighter winds.”