Horses that jump or swerve to get around a little creek or a mud puddle are one of my pet peeves. Even worse, when they'll drag their rider through branches or knock their leg into a tree trunk in order to avoid a puddle.
Maybe it's because the park nearest to me is nothing BUT mud most of the time, so my horse just got used to not being able to get around it and it doesn't even bother him anymore.
Still, there's no reason why you shouldn't be able to get your horse to step over or just walk through a narrow bit of mud.
"Parelli horsemanship is just like painting by the numbers. You need absolutely no skill. You just put this color here and this color there, and when you're done, you have ... a mess no one wants." mp