The American artist, Cassius M Coolidge, painted hundreds of paintings of dogs doing manly things, like smoking pipes , playing poker and so on. They were works with a marked satirical edge but loved by the public for their sheer absurdity.His most famous work 'A Friend in Need' shows dogs playing poker. Two little dogs are cheating the other, big,ugly dogs. That's probably the work Postdog remembers.
The pub's picture may well have been a copy of one of Coolidge's pictures or inspired by him. He was not the only artist to draw humans as dogs but the most successful. He inspired a number of imitators when at the height of his fame, around the end of the C19.