The rail firm announced t closure of the entire train network this morning "due to the huge amount of debris - trampolines, hay bales, trees - on the tracks".
However, it says the damaging winds have now passed and has confirmed that the Edinburgh Glasgow Queen Street, the Glasgow Central to East Kilbride and Motherwell and the Fife Circle lines have re-opened.
Network Rail tweeted: "The damaging winds have now past, we are starting to access the network for damage. We will only open lines when safe to do so.
"We are checking each line now. We are hopeful to get services running later today, although emergency timetables will be in force.
"Some routes will remain unavailable throughout the day as more extensive repairs may be required & passengers should check before the travel"
Police have also downgraded the red alert 'don't drive' warning to a high risk of disruption for all areas except Dumfries and Galloway.
A statement on the Police Scotland Facebook page said: "We are advising drivers that conditions for travel are extremely poor and there is a high risk of disruption for road journeys in Scotland. If you do travel, you are likely to experience significant delays.
"Congestion caused by vehicles may restrict emergency, recovery or winter maintenance vehicles from providing essential assistance or from clearing roads
"Drivers of HGVs should drive with extreme caution and be aware that you may be requested to park at a suitable position by the police
"Winter driving is a question of common sense and drivers should ask themselves if they really need to travel when conditions are poor. No-one should ever place themselves at risk on the road and it may be worth considering postponing your journey or making alternative arrangements such as delaying travel until conditions improve or using public transport
"If you are travelling on the roads you should ensure you and your vehicle are adequately prepared for the conditions, making sure you have sufficient fuel and supplies such as warm clothing, food and water in the event you are delayed for several hours. Charge your mobile phone and plan your route as well as alternative routes."
Winds reached 59mph in Edinburgh and 63mph in Glasgow. Police Scotland said snow is affecting the B976 Crathie to Gairnshiel road in Aberdeenshire.
Homes in Great Yarmouth, Norfolk, were evacuated after officials warned that the lives of people in the region could be at risk from the worst coastal tidal surge for over 60 years.
Essex Police have also said that parts of Jaywick, a small seaside village near Clacton, will be evacuated.
On Scots roads, police have warned that conditions for travel are extremely poor during the morning rush-hour and spoke of a high risk of disruption across Scotland, particularly in the west.
It is understood police have charged a number of drivers with careless driving for ignoring safety restrictions at the Forth Road Bridge.
The A83 Rest and Be Thankful was closed due to an overturned lorry.
The Erskine Bridge has also been closed, while the Skye Bridge and Kessnock Bridge have been shut to high-sided vehicles.
The Forth Road Bridge and the Tay Bridge have re-opened to everything except double-decker buses.
The high winds also disrupted ferry services.
Some schools were closed after problems with power, bus services, or for structural safety reasons.
The winter attractions on Princes Street were also closed.
Thirty seven flights have been cancelled at Glasgow Airport. British Airways has cancelled flights between Glasgow and London until this afternoon.
Around 20,000 homes are without power as rain and winds gusting up to 114mph batter the north of Scotland.
In the Highlands, gusts of 93mph have been recorded at Altnaharra, rising to 106mph at Glen Ogle and 114mph on the slopes of Aonach Mor near Fort William.
The Met Office issued amber "be prepared" wind warnings for most areas of Scotland.
The Scottish Environment Protection Agency (SEPA) has issued a number of flood alerts and warnings, with a focus on possible flooding on the east and west coasts.
Severe flood warnings are in place for Skye and Lochaber, Caithness and Sutherland, Tayside, Central Scotland, Fife and Edinburgh and the Lothians.
The AA said its severe weather team was being deployed in Scotland to deal with coastal flooding.
Darron Burness, head of the AA's flood rescue team, said: ''Coastal flooding is particularly dangerous because of the risk of high waves and very fast-moving water.
''I would particularly warn motorists to avoid coastal routes where the combination of high winds and flooding with sea water will be life-threatening.''
Forecaster Laura Caldwell of MeteoGroup said: "We could see wind gusts mainly in western parts over exposed areas getting up into 90mph.
"There will be really strong winds pushing widely across Scotland as the weather system moves through.
"There's going to be quite a bit of heavy rain mainly in the morning, then that will clear away with snow showers following behind."
The Scottish Government's resilience operation has been activated to deal with the situation.
ScotRail services are not expected to run on 20 routes, including the West Highland lines, the Edinburgh to Perth via Kirkcaldy route and the Ayr to Kilmarnock stretch.
In addition, services are not due to operate until at least 4pm on the Glasgow Central to Ayr, Gourock, Largs, Wemyss Bay routes and Dalmuir to Balloch and Helensburgh.
Reduced timetables are in operation on main commuter routes such as Edinburgh to Glasgow Queen Street, Perth to Inverness, and Edinburgh and Glasgow to Aberdeen.
ScotRail has asked people not to travel if their journeys are not essential.
Train operator East Coast is advising passengers to allow extra time for their journeys. It will run a revised timetable throughout the day.
The 50mph speed limit for trains is in place as a "precaution".
Network Rail is expected to have hundreds of engineers out across the network ready to react to problems and clear any fallen trees.
David Dickson, Network Rail area director for the west of Scotland, said: "Safety is our number one priority during such severe weather. We will be monitoring conditions on the ground closely."
Police Scotland has warned that motorists are likely to experience significant delays.
Superintendent Iain Murray, head of road policing, said: "High winds and driving rain will make driving conditions difficult, particularly on open roads and over bridges.
"If you must travel during rush hour, allow plenty of time for your journey and drive with care to the road conditions."
Power companies have engineers ready to deal with any power line issues or general supply disruption around the country, the Scottish Government said.
All workers on Buchan Alpha oil platform, 83 miles off the coast of Aberdeen, have been flown off the platform because of the weather forecast, operator Talisman Sinopec Energy UK confirmed yesterday.
Ferry operator Caledonian MacBrayne advised ferry travellers to take the severe forecasts into account when planning journeys over the next few days, and air passengers are being advised to check with airports and airlines before travelling.
SEPA has issued 12 flood alerts and nine flood warnings covering both sides of the country.
Marc Becker, hydrology duty manager for SEPA, said: "A combination of high tides and storm surge will result in a risk of flooding in some coastal communities along the Firth of Forth, Fife, East Lothian and Scottish Borders coast during this afternoon."