Northern and Virgin services between Doncaster and Leeds have already been cancelled due to overhead line problems and Virgin has now extended a warning to the East Coast Main Line between London and Scotland.
A spokesman said: "Due to the extreme weather conditions we are advising customers NOT to travel today or tomorrow
"Customers with tickets for 28 Feb or 1/2 March may defer travel until a later date - a further update will follow shortly.
An earlier message said: "Due to damage to the overhead electric wires between Wakefield and Doncaster services are blocked. We strongly advise customer NOT to travel today!"