I suggest that the term "skinner" was applied jocularly to persons handling any type of draught animal--horse-skinner, bull-skinner, etc. Some posters have pointed out that draught animals, mules especially, were too valuable to be flogged raw, but this was the case up to a certain point only. A team in prime condition was too precious to mutilate--not so your broken down old screw. Pre-automotive-age writings abound with descriptions of the nasty techniques used to get one more season of work out of Dobbin before he plods through the gates of the pie factory. So any teamster was liable to being teased about cruelty, whether he actually was cruel or not.

Surprisingly, everyone on this thread assumes that Muleskinner Blues is about the freighting business. No, it is about industrial development projects like logging and road-building where the mule teams provided traction for machines like skidders and graders. "What you want me to bring you back?"--the workers are living in camp, not transporting goods between population centres.

Finally: a drover is in charge of a drove; a driver is in charge of a vehicle.