We cheated and took taxis to and from the lake (about US $3 each way).
Once there we were "accosted" by a large group of young people who wanted photos with us. It wasn't a scam (maybe a sort of Chinese scavenger hunt) so we joined in and asked for our own photo.
They asked to "sign" their book with red-inked thumbprints, and to write an inscription in English ("I hope the weather will be better tomorrow"), which we happily did in our personal quest to improve international relationships.
From there we wandered some more, enjoying the misty views.