Scotland's main train operator warned services would remain suspended on some routes today and run at reduced frequencies on others because of the freezing conditions.
ScotRail said trains on the main Edinburgh-Glasgow line would remain half-hourly, with services every two hours between the cities and Aberdeen.
However, no trains will operate north of Inverness, and on the Edinburgh to Bathgate, Newcraighall and Shotts lines.
A spokesman said: "We are running as many services as possible despite the extreme weather conditions and when road travel is difficult."
Edinburgh airport said it expected to operate normally today after being shut for much of Monday. A spokesman said: "Everything is going well. We're fully open." Aberdeen airport was also optimistic. Its spokeswoman said: "As long as the snow stays away, things are looking good for the coming days."
However, Glasgow airport warned passengers to expect continued problems. A spokesman said last night: "If you are travelling from Glasgow airport tomorrow, please check with your airline regarding flight information. Delays and cancellations are expected."