A Met Office yellow warning for snow is in place until Saturday night for much of Scotland, Northern Ireland and the north east of England, while wind and rain are forecast for Wales with high winds expected on the south coast.
As much as 10cm of snow could fall on higher ground, according to forecasters.
Police Scotland issued a warning to motorists as road conditions worsened on Saturday morning.
A statement said: “There is a yellow weather warning in place for many parts of the country today and many areas are waking up to wintry weather conditions.
“Take care on the roads and be prepared for your journey. Slow down and drive to the conditions.”
Several cars were involved in an accident on the M77 southbound at the Maidenhill exit slip near Newton Mearns, while part of the M8 was flooded at Paisley.
Met Office meteorologist Luke Miall said: “We’ve got quite a few weather warnings in place for today across the UK.
“In Scotland we are likely to see a good covering of snow above 200 metres or so where we could see 2cm to 6cm and perhaps as much as 10cm above 400 metres.
“It’s mainly higher ground but that will affect some of the routes that travel across the Highlands and central parts of Scotland.
“The other warning we have in force is for wind and that covers pretty much everywhere from north-west England down through Wales and then southern counties of England including London.
“Here we will see some pretty strong winds through the day gusting 45mph to 55mph quite widely within that area.”
He said exposed and coastal areas could see gusts as high as 65mph.
He added: “The reason for all this is we have an area of low pressure which is moving its way in and that will continue crossing Northern Ireland and parts of southern Scotland.”
Heavy snow also fell in parts of Northumberland overnight covering part of the A1 at Alnwick.
Temperatures will vary throughout the UK from around 12C to 13C in the south while some areas of Scotland will struggle to get above freezing, Mr Miall said.
The worst of the wintry weather is expected to be over by Saturday evening with a more settled picture for Sunday.