I don't think that there is a rule that ex officio members can never vote. I think it depends on the committee or board and what they've decided on. An ex officio member may be allowed to make a motion, second a motion and vote as well.
I think another issue that is confusing for some is what happens when let's say the President of a board is an ex-officio of another board or committee. Some people think that just because they hold the position of President, they will also have the right to chair and lead other boards that he or she is a member of. But that is not the case at all. No matter what position that person holds elsewhere, an ex officio member is just a member, not the chair.