Hi Charlotte, I can not say with any certainty & this card is not dated so you will have to guess from the clues on the picture.
I will try & find out for you as I will be in Grassington tomorrow visiting my daughter.
As far as I know there has been a Wilson's Arms in Grassington since the coming of the railway in 1902. It is in actually in Threshfield and is now a retirement home. There is a postcard for sale, on ebay at present, which probably shows the Wilson Arms in the 50's.
Ben