Casgliadau Celf Arlein

I have a painting which is almost identical! I inherited it from a Welsh cousin. it is purported to be painted by my 2 x great grandfather Taliesin Williams. the cousin who left it to me wrote that she had given 5 other similar oils to The National Library but I can't find any details.

I have a small painting of a cottage snow scene signed T Waters. It belonged to my grandfather, Thomas Coggins, who lived in Plas Watford, Caerphilly and died in 1945. He was a well known Cardiff auctioneer and acquired many items via his saleroom. I note that the artist Thomas Waters was active around Caerphilly and signed his work T Waters. Perhaps there is no connection but it does seem an odd coincidence. Have you any advice how I could pursue this?