All schools in Glasgow, North and South Lanarkshire, North, South and East Ayrshire, East Renfrewshire, West and East Dunbartonshire and Inverclyde were closed.
Parents in Glasgow woke to discover a decision had been taken overnight to close all schools and nurseries.
A notice on the Glasgow City Council's Twitter site said: "All Glasgow City Council schools will be closed following weather update from Scottish Government and Met Office."
Renfrewshire schools were due to close at 1pm but parents were told they could choose not to send their children to classes.
Strathclyde University cancelled all classes and advised students not to travel in.
The Glasgow Loves Christmas attractions in George Square – the big wheel, fairground, bar, ice rink and stage area – were all shut because of the severe weather. A spokesman for organiser Glasgow Life said: "We have to be sensible and take the right precautions."
Road and rail services were also hit as forecasters warned the winds would get stronger throughout the day, peaking at 100mph in some areas.
The Scottish Government's Resilience Committee met and ministers and officials from the Convention Of Scottish Local Authorities received the latest advice from the Met Office's chief forecaster and the Association of Chief Police Officers (Scotland).
It showed winds gusting up to 90mph were due to hit west Scotland, the Central Belt and large parts of the south of the country.
The Met Office issued its highest red-alert warning for winds of at least 75mph and gusts of 90mph in the Borders, Strathclyde, Tayside, Fife, the Lothians and central and south west Scotland.
Red alert is the most serious that can be issued and could mean potential damage to properties and power cuts.
The strongest winds in Glasgow and west-central areas were expected from noon and were expected to stay strong until this evening.
It led Ministers to advise that councils should, in western parts, not open schools, and in eastern areas close at noon, ahead of the arrival of the most dangerous conditions.
Ministers are also stressing that the travelling public should pay close attention to the probability of the "avoid travelling on the roads" warning being issued by police.
This level of travel warning is unprecedented for high wind situations.
The Scottish Government said it was possible some key routes were likely to close, and police may warn motorists to avoid travelling altogether.
There were reports of early morning disruption in East Kilbride.
Drivers were warned of delays on the A726 Queensway due to an overturned lorry between B761 West Mains Rd and Redwood Drive.
There were reports of localised flooding in Lochwinnoch, between Kilmacolm and Bridge Of Weir, in Renfrewshire, and Switchback Road, Bearsden.
The carriageway was just passable on A8 Greenock Road in Langbank at the B789 Main Road junction, because of flooding.
Bus firm McGill's announced it would be cancelling all services from 2pm due to high winds.
Bosses at Glasgow Airport said they were operating as normal, but were monitoring the weather situation closely.
The specific advice is that conditions for travel could be dangerous and travellers could experience severe delays of several hours or more.
In particular, high-sided vehicles, HGVs and buses should not travel in the periods specified.
Although the utility companies have put in place severe weather contingency plans, including the drafting in of extra staff to carry out emergency repairs as quickly as possible, ministers heard that the very high winds could also have an impact on power supplies.
Deputy First Minister Nicola Sturgeon said: "We can expect very severe gales, at wind speeds not seen for many years, across large parts of western, central and southern Scotland throughout today.
"On the basis of the earlier Red Warning from the Met Office, some councils had already taken the precaution of closing schools early to make sure parents can safely collect children before the most dangerous weather and travel conditions arrive.
"In light of the latest forecast, and in particular the timings which suggest the severe weather affecting the west-central part of the country earlier than originally anticipated, some of these closure timings may have to change.
"We are advising councils in all the affected areas to give parents and teachers the earliest possible notice of their intention to either not open schools in the west or to close at noon in the east.
"The decision is a matter for individual authorities, but the warnings are of the highest level of seriousness and we are clear safety has to be the paramount issue."
Assistant Chief Constable Allan Moffat (Central Scotland Police), on behalf of the Association of Chief Police Officers (Scotland), said: "The forecast for such extreme weather means it is probable we will need to close some or all of the major bridges.
"This will inevitably cause disruption on major routes and have an impact on other road networks.
"We will be continually monitoring weather reports and there is a probability that, based upon these updates, we will recommend the public should avoid travelling in the regions most affected by the extreme weather."
ScotRail said speed restrictions of 50mph could be put in place on trains travelling after 10am, with reduced timetables in operation.
The speed restriction is being introduced in case high winds blow debris and trees on to rail lines and damage equipment.
Steve Montgomery, the train operator's managing director, said: "We will constantly review weather forecasts and respond accordingly. Our aim is to ensure as robust a service as possible."
David Simpson, Network Rail route managing director for Scotland, said: "We will have more than 350 engineers out on the network to keep the railway running.
"However, the extreme nature of the conditions, and the impact they can have on our infrastructure, means that a speed restriction is necessary in the interests of safety."