Twenty seven trains have been temporarily withdrawn from service after overnight checks by Arriva engineers discovered significant damage to some of its trains.
The company added that its engineers have been working since the early morning to locate, and then rectify, the section of track or points across the Wales route and on lines into Manchester which has caused the damage and "the work is on going at this time".
However, it is having "a significant impact" on the train company's ability to deliver its timetabled service.
The majority of long-distance Arriva Trains Wales services operating in North Wales, West Wales and the Marches are currently suspended as a result.
Arriva have advised that some services will be operating with fewer carriages and additionally, given the worsening weather predicted over the next few days, they are advising customers to check online before travelling and only travel if absolutely necessary.
The company have apologised to anyone affected, and thank customers for their patience whilst they work to resolve this issue.
Arriva Trains Wales
The company said the situation "developed overnight" and it has sourced some replacement transport but is advising against "non-essential travel".
It added customers whose trains have been cancelled can claim a refund.
The Cardiff Valleys services are unaffected.
The disruption during the cold snap caused frustration for passengers travelling by train.