Storm Caroline, which brought more than 90mph gales to parts of northern Scotland, left an Arctic air flow in its wake, with temperatures plunging across Britain.
About 8cm of snow had already fallen in Aviemore in the Scottish Highlands by dawn. Parts of Northern Ireland, Wales and areas to the west of the Pennines had also seen a covering.
Forecasters said snow showers were likely to become more widespread throughout the day.
A yellow weather warning was in place for ice and snow across much of Scotland.
Met Office meteorologist John West said: “We saw a fairly consistent stream of snow showers overnight and there will be a constant feed ... into Friday.
“We could see some fairly significant accumulations. Broadly speaking we’re looking at 2cm to 5cm, but in more exposed areas we could see 10cm to 20cm.
“It will also be bitterly cold, with highs of 2C or 3C outside those snow showers. But the wind chill is going to make it feel sub zero.”
Cold temperatures are likely to remain well into next week, with forecasters also warning that Sunday could see further heavy snow showers.
The wintry weather comes after Storm Caroline left thousands of homes in Scotland without power yesterday.
Many train services were suspended, cancelled or delayed as a result of the weather conditions, while ferry services faced disruption.
Some flights in the Western Isles were also cancelled.
Very strong winds are expected to continue today, with gusts of 70mph to 80mph at times, especially over Shetland.
A number of schools will remain shut in the Highlands, having closed when the storm first brought high winds on Thursday.