You not liking the thought of it, doesn't mean it doesn't happen

Since the poop is expelled at full speed, it will likely be scattered in various directions, and possibly even reach other sled dogs and the musher who must navigate through the messy ordeal.
Despite the smelly mess, it's just another challenge that can be added to the other challenges that sled dog teams must overcome, on top of all the other glorious adventures in the frozen wilderness.
Fortunately, mushers wear goggles or other protective gear to avoid any flying debris from reaching their eyes.

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