The data ice model does not create history files. The only data associated with this model is the data that is already contained in the input datasets.
The dice5 model creates restart files. The only data on the restart files is accumulated water, which is ice formed by the ocean component that is stored in dice5 so that it can be subsequently melted back into the ocean component (thus conserving salinity). By default the dice5 model does not accumulate ice formed by the ocean, and thus in default mode the dice5 model does not actually need the data on its restart file, although it always creates restart files anyway. The ability to accumulate water is activated by the namelist parameter flux_Qacc. See the Namelist section of this document.
The data ice model generates diagnostic messages which are written to stdout. This output consists mostly of brief messages that indicate how the simulation is progressing and whether any error conditions have been detected. Stdout also contains a record of the values of all model input parameters.