Example insulated pliable door panels or curtains include various internal vapor barriers. The vapor barriers have a relatively high water vapor transmission rate that inhibits water vapor from permeating through the door panel. With such vapor barriers, outer sheets of the door panel can be made of polyurethane or other tough materials that might have an inadequate water vapor transmission rate. In some examples, the vapor barrier (54) encircles or encloses a thermally insulating pad. In some examples, the door panel (12) includes a sleeve or pocket (66) that holds the vapor barrier in place. Some examples include means (58) for draining water that might condense within the door panel (12).