I had no idea, but did a bit of research on Google. I found that "fur & feather" is a term used to describe some of the artificial lures (or flies) used in fly fishing, because these lures are made out of fur and feather; a fur & feather competition would, therefore, be for anglers fishing with this sort of lure. I'm sorry, but I could find no explanation for using this term for golf contests; but would hazard a guess that they might be contests where the prizes were game, such as rabbits, pheasants etc.