A second day of disruption to travel and power supplies is expected as severe weather warnings remain in place for Christmas Eve.
High winds, snow and ice are forecast for northern parts of the country, with the potential for gusts of 70mph on exposed parts of the Scottish mainland and 80mph across Shetland.
Further weather warnings are in place for Christmas Day and Boxing Day with a second storm, Storm Conor, expected to bring more high winds and a risk of lightning to the Western Isles, north-west Highlands, Orkney and Shetland.
At its height Storm Barbara brought wind speeds of more than 80mph and lightning strikes across the north west of Scotland and the Western Isles.
Scottish and Southern Electricity Networks (SSEN) said that as of 9am on Saturday morning, engineers had restored power to more than 21,000 homes.
A lightning strike affected around 13,000 customers in Lewis and Harris, though all homes were reconnected within two hours.
A total of 762 customers remain without power as a result of localised faults on the islands of Lewis, Jura and Shetland.
Dale Cargill, SSEN director of customer operations, said: “Our network has stood up well to the conditions but we won’t be complacent and remain prepared to respond quickly to disruption to supplies, where it is safe to do so.
“The safety of our customers and engineers will remain a priority as we continue to respond to the impacts of Storm Barbara, particularly given the presence of lightning and continuing poor weather conditions.
“We are acutely aware of the time of year and the increasing concern this brings and would like to reassure our customers we will be doing all we can to keep disruption to a minimum.”
Ferry services remain subject to cancellations and revised schedules and many bridges are subject to high wind warnings but ScotRail said it planned to run services as scheduled on Christmas Eve with the possibility of some minor alterations.
The Met Office has issued yellow “be aware” warnings for Scotland’s central belt and northwards on Saturday, warning of wintry showers affecting large parts of Scotland in the morning.
The most frequent snow showers are expected to fall north of the Central Belt with 5-10cm of snow possible on higher ground.
An amber alert for Storm Conor has been issued for the far north of the country on Boxing Day.
Dean Hall, a Met Office forecaster, said: “There will still be strong winds associated with Storm Barbara affecting the north of Scotland into Saturday morning.
“For Christmas Eve there is a north/south split across the UK. We still have very gusty, squally conditions across much of Scotland and the north of England and Northern Ireland with further showers, some heavy at times and turning wintry over higher ground.
“Through the day the next weather system is coming in which is the start of Storm Conor, that’s going to bring more persistent rain in Northern Ireland, Western Scotland and North West England.
“That will herald the arrival of Storm Conor through Christmas Day but the main impact will not be realised until Boxing Day.
“On Christmas Eve England and Wales will get away with a much drier and brighter day.”
Scotland’s transport minister Humza Yousaf said: “We would urge everyone to check the latest sources of information before they travel and keep in mind that the situation can change quickly.
“They should leave plenty time to get to where they need to be and the transport operators are doing what they can to help people arrive at their destinations and get any last minute festive shopping done safely.
“We shall be continuing to monitor the situation over the festive period including Christmas Eve, Christmas Day and Boxing Day to make sure that the most reliable and relevant information is being communicated to people as early as possible.”
People can call 105, a free new national phone line, if the weather damages their local power network and affects electricity supply.
The number is available to people in England, Scotland and Wales, regardless of who they buy electricity from.