Its Mr., according to the good blue book. President trumps everything. All the Wilson letters I'm finding online are using Mr. to address him as well, like this one.

We have a few Wilson letters in the archives actually (I'm at work) that are pre-presidential, when he was working at Princeton, and it looks like he was addressed as "Dear President Wilson" not "Dear Doctor Wilson," at least by our president. He addressed our president back as "dear president" too, so there's that. We don't have any post-presidential letters unfortunately, and now I'm curious if he went to Dr. in professional life after being president. Dr. for non-medical doctors is was? "incorrect" in social usage (like wedding invites) though, so he probably got addressed with Mr. most of the time.