We did have an icing problem on the nose of the C-124. The ice would form on the mickey mouse radar dome (actually this was a cover over our APS 42 radar antenna) as you can see on this photo of 52-1053. The ice would also continue to build up down below the radar dome and form on the nose clam shell doors.
In 1963 on a flight from Athens to Chateaurox we had a tremendous amount of ice form on the nose and clam shell doors. The loadmaster and 2nd flight engineer took a couple wheel chocks and went forward inside the nose and knocked the ice off.
Our fix for the problem was "avoid flying in known icing conditions". I remember during a trip to Tehren, Iran, we sat in lovely Incirlik Turkey 4 days awaiting weather to clear over the mountains in northern Iraq.
Also, in January 1965 a good friend of mine died in the crash of 52-1058 when it struck a mountain enroute from Aviano to Athens. The official report stated navigational issues. However, since they were in weather through the mountains, I always thought icing on the nose may have caused the problem.