Engineers have still to clear the line between Aviemore and Inverness after a freight train derailment last week. On the Inverness to Aberdeen line, replacement buses have been reinstated between Inverurie and Elgin.
A spokesman said: "We are working with Network Rail to deliver the most resilient service possible across the network."
He said extra staff were being deployed to keep trains running despite the snow and low temperatures.
Councils across Scotland are assessing conditions and will make decisions on whether schools badly hit by the weather will reopen on Monday.
Scottish Borders Council has already cancelled a series of council meetings due for next week.
In the Highlands, firefighters used slings and a digger to rescue a horse that went through ice into a river near Thurso. Fire crews have also been dealing with a spate of chimney fires with people burning more fuel to keep homes warm.
Praising the work of volunteers, the Scottish government said the government, local councils and public services also needed to continue working together to get the country through the cold weather.
It also hailed the work of the Community Off-Road Transport Action Group (COTAG), who have been providing support in the north east of Scotland.
Volunteers in the groups have delivered meals on wheels to the elderly, driven nurses who were trapped in their homes by the snow into Dr Gray's Hospital in Elgin and have also rescued more than 20 vehicles which were stuck in the snow - including one council gritter.
Rural Affairs Secretary Richard Lochhead said: "The exceptional weather has brought out the best in people with volunteers dropping everything to help their fellow citizens in their hour of need. Society owes a huge debt to our snow heroes."
But Labour said the big freeze had highlighted the need for the Scottish cabinet to include a champion for older people.
Deputy Labour leader Johann Lamont claimed too little had been done to help senior citizens trapped at home in the icy weather.
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