I think that had the actors worn simple jackets in the "freezing cold" room, the audience would notice that there is no visible exhaled breath coming from the actors.
I've seen plenty of "cold" scenes in movies with no visible breath, and it never looks out of place. The same goes for day-for-night shooting and other tricks—audiences have come to understand the cinematic shorthands, like blue lighting for moonlight or cold in the same way they understand something as unnatural as cuts and dissolves.
Also... it is not necessary to take an entire movie set down below freezing to get visible breath. The crew working on 2010: THE YEAR WE MAKE CONTACT discovered that humidity is the key (CINEFEX no. 20, p 40). In other words, it is possible to have a bitingly cold real-world situation when breath is not visible because the air is too dry.