The red warning which was in effect yesterday has since finished. The amber warning was initially due to run until 6pm but has since been extended until the following day.
A yellow warning will be in place until Monday as experts predict the hazardous weather to continue across the weather.
Road conditions will continue to be extremely difficult and potentially dangerous throughout the day after snow continued to fall overnight.
Rail, bus and air travel will also be subject to significant cancellations through the morning peak and into the afternoon tomorrow.
Edinburgh City Council said a full gritting night shift would cover the city’s priority one routes.
Twenty-two lorries and 11 mini-tractors will be used across the Capital tonight to treat more than 600km of roads, pavements and cycle paths.
Edinburgh Trams has announced they are running free services for the second consecutive night to help keep the city moving.
Trams will run from every 30 minutes between midnight and 5am tomorrow, free of charge.
Managing director Lea Harrison said: “With severe weather disrupting most other transport options, it’s important we do all we can to help the public get to where they need to be.”
Council chiefs said care staff have endeavoured to visit frail, older or disabled people who rely on care provided in their homes.
Hundreds of service users and their families have been contacted to ensure they have the support and food supplies needed.
Council leader Adam McVey said: “We are making every effort to keep the city moving in spite of severe weather, though we have had to make some decisions to cease services for the safety of the public and our staff.
“I would like to take this opportunity to thank the many staff from across the council who have persevered through the snow to deliver the services most needed by the people of Edinburgh.
“From the gritting teams ensuring our roads and pavements are passable to social care staff visiting some of the most vulnerable people in our society, or the contact centre operatives answering queries out of hours, their work and dedication is essential to running the city.”
All schools, nurseries and early years centres, as well as libraries and community centres, across Edinburgh will remain closed tomorrow.
Neighbourhood offices, museums, galleries and monuments and all Edinburgh Leisure venues are remaining closed, while waste collections are suspended until further notice.
Deputy First Minister John Swinney said: “Conditions continue to be treacherous across much of Scotland, which has led to the decision by the Met Office to extend the Amber warning for snow overnight and through the Friday morning rush hour, signalling the potentially life-threatening nature of the extreme weather.
“Throughout today and into tomorrow morning, the clear and unequivocal advice for people in affected areas is not to travel unless it is absolutely necessary to do so.
“Clearly there are pressures on our emergency services and we thank those individuals for going above and beyond in difficult conditions. Work is also underway, as a matter of urgency, to ensure essential staff in our hospitals can get to work.
“I would encourage employers to continue to show flexibility for their staff, because safety is paramount. I would urge people to continue to look out for the vulnerable in their communities during these difficult conditions.”
Police Scotland Superintendent Helen Harrison added: “We are now 24 hours into the red and amber-related advice not to travel on the roads and rush hour last night was noticeably less busy thanks to people heeding our message. It remains the same this rush hour coming – do not travel.
“Many of those people who did go out yesterday faced treacherous conditions, blocked roads, being stuck in their vehicles or even being involved in collisions. We do not want anyone to put themselves or others at risk in these conditions. We are continuing to run a multi-agency command centre at Bilston to coordinate the emergency response to the severe weather with our partners and keep Scotland moving as best we can.
“If you can postpone your journey in affected areas until after the amber warning ceases, currently at 6pm tonight, I would urge you to do so. Many employers were able to allow staff to work flexibly and this approach is needed again today.”