I thought the origin of this phrase certainly included geese but I was very wrong. It actually has its origins in 16th century horse racing. Go figure! Read about it here . Figuratively the phrase means chasing something that probably won't yield any results.

The expression wild and woolly showed up in print in the Missouri newspaper The Sedalia Daily Democrat, December 1875: "W. A. Palmer, the South Bend, Indiana, murderer and paramour of Dolly Tripp, was for several years resident of Clinton. Bill always was one of the 'wild and woolly' kind and would associate with the demimonde." ( source ) The exact origin of the expression isn't known.