If the border cops find out about the conviction, they probably won't let you in. It used to be that if there happened to be a supervisor at your particular port of entry you could apply for some kind of special permit (and pay another $140 US) and they would let you in, but I wouldn't take the chance if I were you.

If you have a passport, they might let you in without running your background, but it's a gamble. I'd suggest making some calls and finding out as much as possible. Lots of people have been turned back at the border for this sort of thing.

P.S. The "prevailing winds" thing is not true. Surface winds can be blowing any direction at any time.