Why Do They Say “Mush” to Make Sled Dogs Go?

If we relied on Yukon Cornelius from the 1964 Christmas classic Rudolph the Red-Nosed Reindeer to teach us about dog sledding, we might be slightly misled. In multiple instances throughout the movie, Cornelius cracks the whip and hollers, “Mush, mush!!” to his dog sled team. But do mushers actually say this?  You might be surprised given that they are literally called “mushers” that no, not really. So why are they called “mushers” and where did the idea that they yelled “mush” to their dogs to get them to run come from?