ambient temp for pulmonary hemorrage?

A plot point in a recent movie involved death by acute pulmonary hemorrage caused by intense aerobic activity at extremely cold outdoor temperature: the very cold air froze the thin alveolar membranes of the victim’s lungs, causing them to drown in their own blood/mucus.

I recall hearing of such a thing many years ago in the context of arctic or antarctic exploration, but had not heard of it since then. It turns out there is a thing called exercise-induced pulmonary hemorrhage, but it’s mostly associated with horses and there doesn’t seem to be a connection to air temperature.

So what’s the straight dope? Is it possible to die from pulmonary hemorrhage if you breathe vigorously in extremely cold environs? Or was this just a movie exaggeration?