How should I insulate the ceiling between floors in a ski cabin?
You are correct. The field of building science is gradually moving away from friendliness toward vapor barriers in exterior walls, and you certainly should not put one in an interior wall or floor. Not a great idea.

In addition, it would make more sense to use batt or spray foam insulation between the floor joists as opposed to cutting rigid foam to fit in those irregular spaces, which would be a nightmare. Finally, most foam insulations are themselves vapor barriers, so if you use foam, you will be creating much of a vapor barrier anyway. For this reason, ideally you would use mineral wool batts (sold under the name "Roxul" in the USA) in the floor joist bays, as they are highly-insulating and vapor-permeable. As an added bonus, they block sound very well too--useful for insulation between floors of a house. I am re-insulating my house with this stuff and just love it. Unlike fiberglass, mineral wool batts are not moisture sensitive, easy to work with, and highly effective.