I think it was simply an expression of free-spirited, spontaneous playfulness, with a humorous hint at "conquering nature" while on a hike. I've certainly seen old photographs of men in trees also. Perhaps there are more photographs of women in trees because back then, it was often the male companion in charge of the camera... but that's just a guess.
Why people today are less inclined to opt for playful portraits of people in trees may have to do with a somewhat changed cultural attitude about what casual portrait photography should look like.