The Met Office has also issued a Yellow National Severe Weather Warning for snow and ice for much of Scotland, Northern Ireland, Wales and parts of northern and western England for Friday - 1-3 inches of snow is likely fairly widely, with 4 to 8 inches in more northern areas.
Forecasters are expecting the storm - the third named storm of the year - to bring gusts of up to 80mph in northern Scotland. Some rural communities could be cut off and power supplies interrupted.
Road, rail, air and ferry services may be affected as cancellations are likely.
A trampoline was blown on the railway line at Patterton in East Renfrewshire, and a gazebo at Coatbridge in North Lanarkshire.
Met Office meteorologist John West said: "Storm Caroline is well on its way across northern parts of the UK".
The storm is expected to last all day, with a yellow "be aware" warning for wind also in force for the southern half of Scotland and northern parts of Northern Ireland.
"The greatest impacts are expected to be spray and wave overtopping which could see flooding to low-lying areas and at-risk properties on exposed sections of coastline", said the organisation's duty flood manager Mark McLaughlin.
Many Western Isles schools were closed along with 55 Highland Council schools and nurseries, with at least two also shut on Friday.
Train services have been suspended between Aberdeen and Inverness, Inverness and Wick, Inverness and Kyle of Lochalsh as well some Glasgow Queen Street routes to the west coast.
Thursday evening, snow showers will become increasingly frequent and heavy across northern Scotland.
Brian Gaze, forecaster for Weather Outlook, said: "Colder easterly air expected from as far away as Siberia means minimum temperatures as low as -16C could be seen this winter in Scotland, with -12C even in sheltered parts of southern England".