ScotRail has urged urge people to go home now as it prepares to shut down part of the network by 6pm.
It said there would be no trains in the red warning area around the Central Belt from 6pm until 10am tomorrow.
The closure will cover lines across the Central Belt and other parts of Lothian and the Borders and Strathclyde, and in Fife and Tayside.
Passengers were told: "Severe weather warning. ScotRail services being withdrawn from now. No services 1800 Weds to 1000 Thurs. Remember to check our app or twitter tomorrow."
A spokesperson said: "Travel home now. We will be closing the railway - it will be run down from 2pm."
ScotRail also issued a statement to customers: "As with other forms of transport across the country, the severe weather has caused significant disruption for the railway.
"Safety is our priority, and is central to every decision we make.
"Customers should head home now, as we are winding down our service early in the red areas.
"There will be no train service tonight or first thing tomorrow morning in the red areas."
The decision follows the train operator cancelling more than 200 services across eastern Scotland and around Glasgow in advance of the snowfall.
The operator has since cancelled more trains in Glasgow, including many at Glasgow Central.
The ScotRail Alliance with track owner Network Rail said yesterday that sets of points, which enable trains to switch between tracks, would be set in one direction to reduce the potential for them to stop working from ice and snow.
This has been standard practice fro several years.
It said: "This will allow us to position staff at critical locations, where they can help keep points and signalling equipment clear of ice and snow.
"On a normal day, our points move regularly to allow different trains to travel on different routes.
"When we are faced with snow and ice, this can increase the risk of a points failure – snow and ice can get caught between the points, which causes delays."