Avoid it for anything outdoors, and don't worry about it on the ship. Cotton absorbs moisture, dries slowly, and makes you colder once wind hits damp fabric. That rules it out for landings, Zodiac cruises and kayaking layers, including cotton t-shirts as base layers, denim under waterproof pants, and cotton hoodies as your main insulation.
Onboard is a different question. Jeans, cotton shirts and casual clothing are fine indoors if they suit the ship's dress code. The distinction that matters is expedition clothing against onboard clothing, not banning a fabric from your suitcase.
For excursions use merino, fleece, wool blends or technical synthetics. Check the labels before packing, because a garment sold as warm or outdoor can still carry enough cotton to perform badly when wet.