According to wikipedia the 600 series has CATIII capability:
https://en.wikipedia.org/wiki/ATR_42#ATR_42–600
From some googling a video you might like, it is CAT II but still very impressive.
Quite a few airports would need to shut down several days per year without CATIII.
Regional airliners in the US are often only equipped CATI or CATII but seems like Dublin and destinations are foggy enough for Aer Lingus to equip CATIII. (Or maybe it was just CATII hard to know)
Most A320/B737 and bigger aircraft are usually CATIII capable or it is at least a customer option. Not all but most operators qualify their crews to perform CATIII.