I had a swarm move into a stack of boxes once that had no bottom board on it. They were doing fine. But I'm not sure I would do it on purpose in my climate.
I am sure at some point during the year having an open bottom would help. And at times they are a bad idea. I am sure some one has made a multifunction bottom board that can have different inserts for different conditions.
Thanks for all of the input from everyone. I was refering to Charles Martin Simon's bottomless beekeeping article.
I now realize that I should have explained myself better. Yes the hives would be on a frame to keep them off the ground. For some reason this does seem like a good idea to have no bottom board, but I do see a mutitude of problems in the colder months as well as robbing. I think I will stay with bottom boards for now. Thanks everyone!