I don't really get the point of "free transit on certain days," especially as those things are always intended to benefit non-regular users of transit. If you want to encourage people to use mass transit on New Year's Eve, do so by committing to providing much better than normal overnight service. Don't increase the subsidy by not charging people, increase the subsidy by providing better service.
...adding, one good reason to provide free service is to speed boarding times when demand is unusually high.