Virgin trains are urging east coast customers not to travel.
Service resumed on the west coast service but Virgin trains have urged caution to those on the east coast.
A Virgin Trains spokesperson said: “Due to extreme weather conditions on our east coast route, we are advising customers not to travel today or tomorrow.
“We’re working hard to look after our customers in whatever way we can and customers who have booked to travel will be able to use their tickets next week.
“On our west coast route, we have resumed services to and from Scotland today though trains to and from Edinburgh remain cancelled. Customers who have booked to travel to or from Edinburgh or Glasgow can travel on any Scotland services until Sunday 4th March.
“Customers travelling across both our east coast and west coast routes are advised to check our websites for the most up to date information before going to the station.”