Natasha's parents issued a statement in which they said they were "devastated" at the loss of their "beloved daughter", adding that she would "be greatly missed by all who knew her".
The school coach had been carrying 39 students from Lanark Grammar School, five members of staff and a driver when it left the road and finished on its side just after 0600 BST on Wednesday.
They had been due to travel to Alton Towers theme park, in Staffordshire.
Three other children were seriously injured and two people were airlifted to hospital in Glasgow.
NHS Lanarkshire said 44 people in total had received hospital treatment following the crash, 19 of whom remained in various hospitals around Lanarkshire and Glasgow.
The health board said all the patients were in a stable condition.
South Lanarkshire Council said its "thoughts and prayers" were with Natasha's family.
Strathclyde Police said the crash was being investigated but road conditions had been "horrendous" and snow "had a part to play".
Parent Susan Thornton, who chose not to allow her son Adam to go on the outing, questioned why the trip had gone ahead given the weather conditions.
She told the BBC News channel: "I was very surprised. It was midnight when I made the decision. When I woke it was clear that it had been snowing through the night."
The remote location and snowy conditions hampered efforts to reach passengers after stuck on the Edinburgh to Inverness train.
It became stranded between Carrbridge and Slochd stations on Wednesday evening on one of the UK's highest railways, about six miles north of the Aviemore ski resort.
A Northern Constabulary spokesman said all the passengers were well but added that it "has been difficult to reach them because of the location".
First ScotRail said a snowplough had cleared the track and a four-coach relief train carrying food and water was being sent to the area to collect those on board.
The company said it expected to get the passengers to Inverness by 0330 BST.
A spokesman said: "People have been on board for about six hours - they are tired and fed up, but the driver has said no-one is in distress."
Superintendent Iain Murray of Strathclyde Police on the bus crash
Earlier on Wednesday, police said they had rescued 300 people from vehicles, including a school bus, stuck in snow on the Glenshane Pass, near Londonderry.
Ch Insp Steven Cargin, of the Police Service of Northern Ireland, said the rescue operation had involved police, mountain rescue and coastguard workers.
Motorists were taken to Dungiven Leisure Centre, in Derry, only for a power failure to strike, forcing them to relocate to nearby Limavady and Maghera.
Some had spent 10 hours in their vehicles without food and drink.
Jackie O'Hagan, who was one of those rescued, described the experience as being akin to "Armageddon".
Police said no-one had been injured in the operation, although nine people had refused to leave their vehicles.
Officers said driving conditions across Northern Ireland were "treacherous" and advised motorists to slow down. A severe weather warning lasting until 0800 BST on Thursday has been issued for icy roads.
In other developments:
Vehicles were stuck in various places in Aberdeenshire overnight on Tuesday
Some roads were difficult or impassable in the Borders, and in central Edinburgh two men had a lucky escape after a tree fell on their car
The East Coast Main Line, which has been closed between Edinburgh and Berwick-Upon-Tweed, will resume on Thursday with minor timetable changes
There were no ferry services between Scotland and Northern Ireland
Flights to and from Belfast International Airport have been subject to cancellations and delays
Operation Stack, where lorries headed for France are parked on parts of the M20, was put into practice by police in Kent after bad weather hit ferry crossings.
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