The popular locomotive was booked to haul services on the heritage line this weekend, on both March 3 and 4.
But an amber warning for more snow has forced the NYMR to delay its visit.
The locomotive is still expected to work the line from March 6-11, including additional trains at 9.30am and 12.40pm on March 9 for those whose bookings were cancelled.
NYMR general manager Chris Price said
"The safety of our passengers and staff is paramount and despite the tremendous efforts to ensure this event went ahead, concern over customers travelling to departure stations must come first."
Passengers who had booked trips on Tornado have been contacted by the NYMR.