>>45263083Both cover Steel and other Ice types, Fighting covers Rock and Normal, which are nice, but Rock can also be covered by Flash Cannon, which also nails Faries.
Fire covers grass, which is redundant, and Bug which isn't.
Fire is typically a must-have type to cover the likes of Scizor and Ferrothorn. Regice obviously can't come in on Scizor, BUT Regice can be a VERY good lure for it, if you haven't revealed HP yet. Regice probably can't OHKO Ferro, so that's mostly irrelevant.
The last thing to consider is that HP is ONLY 10 more BP on a SE hit than Ice Beam, and trades that 10 BP for the freeze chance, which, in my opinion, is a shitty trade.
So with that in mind, run HP in mind for the types that Ice Beam is NVE against, or for those 4x weaknesses. The former is Steel and Ice... which are already accounted for, the latter is a decision of whether you want to be prepared for the likes of Bastiodon, Aggron, Alolan Raticate, and Bisharp, or Abomasnow, Scizor, Ferrothorn, and Forretress.
Remember that 4x weaknesses that Ice Beam is also SE against are only a 20 BP difference, so don't consider things like Leavanny or Parasect.