Gysbreght
It appears to me that two issues are getting mixed up. In the first case the aircraft is in normal law and there is no icing of any AoA sensors or Pitot tubes. But due to change in AoA externally without any action on side stick by the pilot the alpha prot protection is activated. This will cause speed(AoA) to latch and the aircraft will normally descend but if AoA decreases because of outside airflow on the wings the aircraft will climb. This can be unlatched by pushing the stick forward. The second case is AoA probes are frozen at low speed (high AoA). When the aircraft accelerates to higher Mach the alpha prot threshold is decreased as the CL max reduces and that triggers erroneous alpha prot which cannot be unlatched. In this case you put the aircraft into alternate law and override the protection. This case is not going to put the aircraft in serious dive but normal descent at constant speed as it is latched. At lower altitudes at equatorial region temperatures ice will melt and situation should become normal.