What an odd subject.
Why anyone would think a small, snorty, bow legged, flat faced dog with bugged eyes would make a good barn dog, I can't imagine. Livestock and small, slow critters with health issues are not a good combination.
Pugs are cute in a fugly sort of way, but if you want a small dog that's good for the barn, get a Jack Russell Terrorist (not a typo).
Pugs are supposed to be house pets. Let's keep 'em there.