The biggest potential problem in cold (below freezing) temperatures is loss of battery power. All batteries perform less effectively when they get cold. If the batteries are kept reasonably warm, e.g. in an inside pocket next to your body, the Box will work just fine. The FC member bluntfaced posted a review which said, in part:
As far as using the unit at high altitude, it rules. I've used it on chairlifts and gondolas many times as well as in lodges at the tops of mountains. It works great in the wind as well. The only problem with the cold is it seems to shorten the life of the batteries ever-so-slightly. I kept my battery case and box in another soft case under my main ski pants and against my leg to keep them from getting too cold. This seems to work very well. The only time I had problems was when it was snowing really hard. Snow accumulates on the box and melts. I only used it once in these conditions then decided it wasn't worth it. As far as wind goes the box is the ultimate solution as it does not depend on a lighter.