Forecasters are warning of a danger to life, with gusts of up to 90mph.
Flights and ferry services have been cancelled while dozens of schools are closed across the north of the country.
Rail passengers have also faced disruption, with trains cancelled after a trampoline blew onto the line in East Renfrewshire and services suspended elsewhere.
About 2,000 Scottish and Southern Electricity Networks customers in the Western Isles and about 270 in Aberdeenshire were left without power, but have since been reconnected.
A 73mph gust was recorded at Stornoway Airport while a 69mph gust was measured at Altnaharra in Sutherland this morning, the Met Office said.
Met Office meteorologist John West said: "Storm Caroline is well on its way across northern parts of the UK.
"There will be devastating winds in some parts. More broadly across Scotland there will be 60mph-70mph gusts, but in exposed areas we could see 90mph."
The strong wind warning is valid until 11:55pm today, with an amber warning for northern Scotland.
The Met Office has warned of flying debris that could lead to injuries or danger to life while damage to property is also possible.
A yellow "be aware" warning is in force for the southern half of Scotland and parts of the north of Northern Ireland until 6pm as well.
All schools and nurseries in Lewis, Harris and Uist in the Western Isles are closed to pupils as a precaution while 31 primary schools, five secondary schools and 19 nurseries in the Highland Council area and two schools in Aberdeenshire are shut.
Train services are expected to remain suspended until the end of Thursday between Aberdeen and Inverness, Inverness and Wick and Inverness and Kyle of Lochalsh.
However, by late afternoon, some trains resumed on the Glasgow to Oban, Fort William and Mallaig lines following a safety inspection.
Speed restrictions which delayed trains on the lines from Perth to Aberdeen and Inverness have been removed.
Rail passengers faced disruption after a trampoline blew onto the line in East Renfrewshire.
Train services between Glasgow Central and Neilston were cancelled or delayed while staff removed the obstacle.
ScotRail tweeted: "There is a trampoline blocking the line in the Patterton area. Please remember to secure garden furniture/trampolines if you live near the railway tracks."
The line reopened after the trampoline was removed and services began returning to normal.
Some flights in the western isles have been cancelled.
Caledonian MacBrayne ferry services between Tarbert and Lochranza, Oban and Tiree via Coll and Ullapool and Stornoway have been cancelled for the rest of the day while many other routes are facing disruption.
The Forth Road Bridge and Tay Road Bridge are closed to double-decker buses while the Skye and Kessock bridges are closed to high-sided vehicles.
A North Sea platform shut down production due to safety fears over weather conditions caused by Storm Caroline.
CNR International said it would remove all of the 159 staff on Ninian South, about 240 miles from Aberdeen, from the structure as a precaution.
There have been snow showers across high ground in Scotland.
A mixture of sleet and snow showers will work their way across the whole of Britain this afternoon, with the potential for blizzard conditions in Scotland.
The wintry showers will become more widespread over the next 24 hours, with forecasters also issuing a yellow severe weather warning for snow and ice on Friday.
It covers much of Scotland, Northern Ireland, Wales and parts of northern and western England.