A yellow weather warning has been issued for wintry showers and icy patches on Monday evening and Tuesday morning.
The area covered includes most of Scotland, Northern Ireland and parts of the north of England.
The warning applies from 20:00 on Monday until 10:00 on Tuesday.
Forecasters added it could lead to hazardous travel conditions, with roads and railways affected and the possibility of longer journey times.
Snow has affected a number of routes on Monday, including higher level roads in the Borders, Tayside and Aberdeenshire.
Water levels remain high after several days of rain.
The railway line between Stirling and Perth remained closed on Monday because of the effects of high water levels at Mill O'Keir viaduct.
As the water began to recede, Network Rail Scotland said "the sheer force of the water has damaged the nose of one of the piers".
It added: "Our specialist divers also need to check for damage at the base of the pier, below the waterline. We're working hard to assess and repair the damage so that we can reopen the railway.
"Thanks for your patience."