In an Airbus product if you ice over the pitot tubes with no associated ecam faults the ADC's will accept the erroneuos information. The airspeed will decay, the pitch trim will kick off, the auto-pilot will disengage and the rudder will go into the "low speed" mode. With no rudder inputs from the pilot the yaw dampener will begin to make larger and larger inputs unless a/c speed is reduce. I know this to be a fact because it happened to me in 2006 at FL310. At first Airbus said no way that that could happen and that we had to induce these failures. Thanks to a few hard charging mx types they found some melted pitot heat relays that shut off the pitot heat but did not produce any ecam warnings. I am not saying this is what happened here, just my past experience. My thoughts and prayers go out to those that are suffering at this time and that the FDR and CVR are recovered.