In most cold cities the winter answer is to shorten the walk. In Boise the better answer is to relocate it. The Ridge to Rivers system carries roughly 190 miles of trail into the foothills directly above town, and on an inversion day those trails are frequently in sunshine while the Greenbelt along the river is under grey fog. Climbing a few hundred feet genuinely changes the air you and the dog are breathing.
This is a good match for the breed rather than a compromise. A medium, straight, water-resistant coat handles cold, dry Idaho air comfortably, and a dog rated 4 out of 5 on trainability can be taught reliable trail manners quickly — which matters, because parts of the foothills close seasonally to protect wintering deer and elk, and Ridge to Rivers publishes conditions asking people to stay off trails when they are muddy.
The cost is modest but real: fuel to a trailhead several times a week through the inversion season, and traction underfoot for the human. Set against a winter of daycare bills to burn off an under-worked sporting dog, it is the cheaper option by a wide margin.