Sioe Nadolig Cyw at Theatr Elwy, St Asaph on Saturday and Galeri, Caernarfon on Sunday have been cancelled due to the snow.
S4C apologises for the disappointment and are hoping to rearrange next week if it is possible to do so.
As a result of the decision, Cyw’s television provision will be extended over the weekend with extra programming between 11:00 and 12:00 on Saturday and 09:00 and 10:00 on Sunday morning.
A special live broadcast of Stwnsh Sadwrn at the Waterfront Wonderland in Swansea has also been cancelled because of the winter weather. Stwnsh Sadwrn will instead be broadcast from the studio with Ant, Al and Lois.