CICE can be used in the way DMI use it, but it wasn't designed with that use in mind (they are using a climate model for weather), and that requires a leap of faith to accept in the absence of scientific publication backing it up.
Hopefully I can add a bit of clarity here.
CICE is certainly used within a number of climate/Earth system models (most notably the NCAR CESM) and has traditionally been developed for that purpose, but on it's own, I wouldn't call it a "climate model".
Climate modeling is a boundary value problem, whereas numerical weather prediction (NWP) is an initial value problem - they each have a different purpose. The same model (i.e. code base of physics) could perhaps be used for either application, depending on how it is set up. e.g. a model typically used for NWP could be used in climate mode and a model traditionally used for climate applications could be used for NWP. The UK Met Office / Hadley Centre apply the same "unified" model for both NWP and climate modeling, but (I believe) different aspects of the model are used for given applications. A bit off topic, but just FYI, weather models (e.g. GFS & WRF/NAM and ECMWF's IFS) include sea ice more as a boundary condition for the atmosphere - very basic thermodynamics (often using specified albedo and ice thickness) and no dynamics as concentration is specified from observations.
The more pertinent questions are:
1) can the model physics be applied to the desired scales (grid resolution / timestep). Does the model resolve the required processes for a forecast or climate application and are the assumptions/paramateriztions appropriate e.g. if running at <10km in the atmosphere, you might want to consider a non-hydrostatic formulation. Another example from my more usual area of work (terrestrial modeling): the Community Land Model (CLM, used in the NCAR CESM) was built for a climate model, but is being used for NWP some European models (not ECMWF, which have their own model HTESSEL). If I was building a new forecast system, I would choose CLM over the current NOAH land model that is used within the GFS/NAM/WRF (NOAH was built for NWP).
2) If a model is being used in a forecast mode (as per NWP), how good are your initial conditions? What data do you assimilate and how do you assimilate it?
For (1), to my knowledge, CICE can be used appropriately at the scales applied by DMI (~10km). HYCOM/CICE is used by the Naval Research Lab at 1/12 degree resolution (~9km on a great circle), POP/CICE is used in the Regional Arctic System Model (also at 1/12 degree). MOM/CICE is used within the NASA seasonal prediction system.... and, CICE is used at ~1 degree resolution with POP in CESM. (HYCOM, MOM and POP are all ocean models). The relative skill/ability of CICE vs GIM (in PIOMAS) is an altogether different question.
For (2) you'd have to read the documentation regarding initialization. Also remember that while both DMI and PIOMAS assimilate concentration, they could do so in very different ways and the respective assimilation systems may or may not impact other state variables in the model (... or they may do it in the exact same way).
The main point is that it's not as black and white as "using a climate model for weather".
And as was noted, verification of a model is always useful information.
- Regarding my own "forecast system"; the poster on my web site is outdated... working on better docs (amongst a thousand other things).