The Met Office said “increasingly frequent” snow showers were affecting parts of Scotland, Northern Ireland and northern England.
It said 10-20cm of snow could fall in northern Scotland, Northern Ireland, north-west Midlands and north Wales.
The Met Office has yellow “be aware” warnings in place for snow and ice.
It said across the UK, 2-5 cm (1-2 inches) of snow was likely in the other affected areas.
“The heaviest and most frequent snow showers will progressively become confined to north-east Scotland during Saturday,” it said.
It comes after Storm Caroline brought winds gusting more than 90mph on Thursday, disrupting rail and ferry travel and shutting dozens of schools in Scotland.
About 500 homes remain without power in Scotland as repair teams were stood down for safety reasons overnight.
BBC weather presenter Louise Lear said although the storm-force winds were expected to ease during the night, conditions will remain blustery and there will be a cold start to Friday with temperatures ranging from -2C to 3C (28F-38F).
Pictures of the snow showers have been shared overnight on social media.
The Met Office said: “Icy surfaces are also likely to be an additional hazard, especially overnight and there is the possibility of travel delays on roads stranding some vehicles, while some rural communities could be cut off and power supplies interrupted.”
It warned of “possible delays and cancellations to rail and air travel“.
The Met Office says Storm Caroline’s winds are now confined to the far north-east of mainland Scotland and the Northern Isles, and there could be gusts of 70-80 mph at times, especially over Shetland, on Friday.
BBC contributed to this report.