My experience in commercial twins of a much larger size is that they frequently do not work well if at all as repairs are so expensive
I worked for one company that they were rarely working and if they were you only ever used them for straight and level. If they could they would have stripped them all out but the mod for that was more than the airframe was worth minus engines.
doubt the a/p restriction in icing has anything to do with control surfaces freezing up, ice doesn't usually accrete far enough back on a flying surface to affect hinges
Its not the hinges that freeze up its the balance horn that goes up to the leading edge that gets an ice bridge going along the leading edge and locks it tight. Twin tps' have electric heaters on them and it gets very restrictive under the MEL if they are US.
If icing is involved which if the freezing level was 3000-4000ft he was in exactly the wet sub cooled just need something to stick to area when it all occurred. They will never find out because it will have all melted when it hit the water so the aircraft will show nothing wrong with it mainly because there is nothing wrong with it.
You can fly IFR and not see the ground from 200ft until 200ft at the other end apart from that its inside of a cloud and the only time you will pick up icing is in the first and last 5000ft and we are talking maybe 3 cm thick on the spinners and leading edge in under 5 mins sometimes. You land with lumps of ice banging off the hull from the props and you can feel the boots inflating on the tail through the controls while you flare and the reaction of the back end change as the ice comes off.