No, the right response in the DITV case would be, "We march on, drawing our coats in, shivering in the cold..."
It's not at stake, no, but that doesn't mean it doesn't exist. Dogs is sort of a bad example, as well, as you're rarely, if-ever supposed to be "in conflict" with the environment. It's a game about judgment, morality, and so on. But if I say that the journey is long and unpleasant, I expect the Dogs upon their arrival in town to go to the local inn and get a nice, warm bath. Or a hot meal. No stakes, no conflict...just plain ol' being in character.
I don't care if you're gamist or simulationist or narrativist or any of that nonsense. This is roleplaying. If you really believe that if it doesn't give you a penalty, or affect a dice roll, or change a statistic, that it "effectively doesn't exist", then I can't imagine how your game must be. Looking over the transcripts from my game, at least half of game play (at least) is just simple roleplaying with no dice rolling. Conversations between characters and other things of that nature. That's a very real, extant part of game play. It matters.
This isn't a style of gaming. I'm entirely willing to toss different styles different bones, even if it isn't my own taste. That's just part of GMing.
This is basic. This is practically as basic as rolling dice.
but you'd do well to represent things that are mechanical mechanically.
And we come full circle again. The interaction of off-screen NPCs? Not mechanical.
The mechanics are how the PCs interact with the world and the world interacts with them.
Full stop. The world interacting with the world? All in the DM's head, described as best he can, decided however he damn well pleases.
EDIT: Hell, they're not even exclusively how the PC's interact with the world. They tend to only crop up when there's something at stake- a resource, survival, a beloved supporting character. I wouldn't use the rules to establish how the PC goes and gets lunch from the local restaurant, but I certainly might have a scene with the PCs going to get lunch.