You'll need to help push the Mule out of the mud by repeatedly clicking on the animal and waiting for the meter above its head to fill, just as with every other injured animal in the game. Once you get to a certain point, you'll be told you don't have the strength to continue, and you'll need to assemble a crew of muscle, consisting of your FrontierVille neighbors, to finish the job. You'll be able to send out individual gift requests to six or more friends, with the first six that respond each filling a position on the crew such as pulley operator, supervisor, mule whisperer and so on. Only after you've gathered enough friends can you finish the job of rescuing the poor Mule from the mud.
All told, this does seem like a bit easier of a setup than the other Injured Critters, as you don't have to risk your friends missing your requests for Critter Milk, berries, etc. on the news feed, and can go to ask help from them directly. In addition, you don't have to wait five minutes between your own attempts at helping. It's nice to see more variety in FrontierVille's Injured Critters, and we can only hope Zynga continues the trend.
Have you received a Brown Mule on your land yet? Let us know what you think of it in the comments.