Doesn't look like an explicit ban on preprints, though Nature might prefer that you not do it. I'm pretty sure I've seen a Nature paper or two appear on the arXiv around the time of publication.

"Nature does not wish to hinder communication between scientists. For that reason, different embargo guidelines apply to work that has been discussed at a conference or displayed on a preprint server and picked up by the media as a result. (Neither conference presentations nor posting on recognized preprint servers constitute prior publication.)

Our guidelines for authors and potential authors in such circumstances are clear-cut in principle: communicate with other researchers as much as you wish, but do not encourage premature publication by discussion with the press (beyond a formal presentation, if at a conference)."

Looks like they say "It's okay to talk among scientists, but don't talk with the media at all until we've released it. We'll pull your paper if you do."