Flight Detent,
Yep !!you are correct that the water seperators 'help' clean the air and try to maintain between 32 and 37 degrees "F" (depending on spec,model) with help from hot air "anti-ice valving".However they have a massive by-pass capability so don't really act as a 'dedicated'air cleaner.Early 737's had a dedicated cleaner (for engines only)that had a constant 'bleed'overboard (hot air)so didn't suffer from freezing.