The yellow warning remains in place until 10am and commuters are being urged to take care on the roads.
They said: "Heavy rainfall expected later Friday, overnight and into early Saturday with falls of 30 to 50mm expected".
Pavements may also be affected, increasing injuries from slips and falls. Some bright or sunny spells are expected where fog has cleared and especially in coastal counties.More news: Winter Olympics: Jenny Jones - history-maker at Sochi 2014
Conditions will become cooler again on what is forecast to be a cold and misty night on Thursday, with frost, fog and temperatures as low as -2 degrees.
The bad weather will continue in to Friday, with strong winds and a spell of heavy rain expected. Afternoon temperatures will range from 5° to 9°, while it will be coldest in the north.
The Met Office stated: "Snow showers will be heaviest and most frequent across western Scotland".More news: Suter helps Wild down Blackhawks
"Top afternoon temperatures 3 to 7C". Windy and mostly cloudy elsewhere too, with the rain spreading eastwards all the while and with some heavy rain in places by dawn.
Britain is wrapping up for another chilly night with temperatures expected to drop to freezing widely with lows of -2C (28.4F) or -3C (26.6F) in rural regions.
"Fog will be quite stubborn to shift and could still be an issue into tomorrow afternoon, there are some places where it won't clear all day".More news: Bears bring back defensive coordinator Vic Fangio on 3-year deal
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