There isn't any more water. Merely that you have say +5deg ambient, in the carb it is now -25deg. At -25deg, ice will be much less likely to stick. My understanding is that ice sticks because when it impacts, the impact pressure causes the ice particle to quickly melt and then it re-freezes.
OK, I understand the proposed mechanism, I think, but I don't believe it. The kinetic energy of a 100 kt ice particle is about 1 J/g which is worth about 0.25 degC. Even if the ice particle impacts a surface and just stops (which is highly unlikely), the "impact pressure" will be effective only in marginal cases.
Ice doesn't stick. Supercooled liquid water sticks.
Unless the air is cooled sufficiently to cause ice precipitate to pass straight through the engine. It appears that with very cold air, the ice particles go straight by the throttle plate without sticking.
But the ice particles need to be there in the first place for this to be a problem, right? Again, I can see how heating up a volume of glaciated cloud could cause icing where none would otherwise be observed, but I can't see how heating up a volume of unsaturated air could do so.