OK I'm stumped, without messing up the thread and staying on topic....
When the opportunity arises on the trail? Is it because of cold water?
Now I already know the trail is a rim or top edge trail, but there are springs and pools and if you follow them down after pitching your tent, after a long day?
A mountain stream dip is the most pleasurable "alone" moment. Doesn't require soap but it helps knock the sticky grime. I have done it early enough that the nylon or polypro clothes are dry the next morning...
So weigh in, and keep in mind.... This is about personal hygine and just for a moment - there isn't a trail town available!