So I don't know if anyone has ever come up with a reasonable excuse for Prompto's sudden outfit change in his DLC episode, but I have a theory:
In earlier chapters, when checking out the Greyshire Glacial Grotto (a Dungeon hidden behind a waterfall) the following exchange takes place:
Prompto: The legends say to look behind the waterfall. Ignis: What does the waterfall say? Prompto: I think it says, "come in." [The group checks behind the waterfall.] Wouldn't you know it - an entrance! Gladiolus: Looks like the legend checks out. Prompto: This place gives me goose bumps. Double back for our coats? Gladiolus: What's the point? Little chill won't kill ya.
I propose: after the Greyshire Glacial Grotto, Prompto stuffed his cold weather gear into the Armoury/Armiger/shared magical subspace-pocket, just in case. Then, when that bullshit on the train happened, he hit the snow, rolled and managed to grab his cold weather gear and gun out before Noctis got too far away for him to access it. (Assuming there is actually a distance based cut off for power use.)
(But why would he need his cold weather gear in the first place? They weren't far from Tenebrae? The weather wasn't that cold. - Ah! But there was a mass of daemons and Imperial troops between Prompto and Tenebrae, he knew his best bet was to cut through Shiva's temper tantrum, and meet back up with the others closer to their final destination.)
