The thought process behind the lack of tail anti ice is that the wings will pick it up first (larger X section) and by the time those pick up enough for the tail to start having problems you arent' flying anymore.
But that doesn't make sense, if the wings are heated then they won't pick up ice. The tail still will. And I always though Icing and tail stalls were pretty critical issues, but my guess was that it had something to do with the fact that the Avanti's tail produces positive, not negative, lift.