As a PPL, I would not want to fly in known actual icing conditions, regardless of the kit ...
Firstly, a plain PPL can't anyway because he is limited to VFR only
Also I am not sure what a CPL/ATPL does when it comes to icing. Anybody can be told what to do in a given situation. The license type is nothing to do with this, as far as I can see. One needs to understand the aircraft capability which is what we are trying to debate here.