Very small amounts of insulation in cathedral ceiling, risk of condensation?

A homeowner with an unheated summer cabin asked a building-advice forum about a cathedral ceiling (a sloped ceiling that follows the roofline, with no attic space above it). The cabin sits in a moderate-to-cold climate zone, has a roof that isn't vented, and includes dormers. Right now the ceiling has no insulation at all. The owner wants to add air conditioning for summer use and is weighing whether to add just a little insulation to soften the worst of the summer heat and winter cold.

The usual guidance for this kind of unvented cathedral ceiling is that only closed-cell spray foam is safe, because it blocks moisture from reaching the cold roof deck, where it could condense and cause rot. The homeowner's question was whether a thin layer of a breathable insulation, such as 2 inches of rockwool (a mineral-fiber batt, here rated around R-8, a modest insulation value), would still create a real risk of condensation inside the ceiling. If the risk turns out to be significant, the plan is to skip insulating the ceiling entirely, since this is a rustic cabin the owner doesn't want to remodel heavily.

As of this posting, the question had not yet received any answers. Anyone with a similar unvented cathedral ceiling and cabin-style, part-time use should know that partial, permeable insulation in this kind of assembly is exactly the situation where condensation risk needs careful evaluation before work begins, since the wrong approach can trap moisture in the roof structure.