A(n) _____ usually refers to the horizontal decorative trim over a door or window, or at the top of an exterior wall.

The term that refers to the horizontal decorative trim over a door or window, or at the top of an exterior wall, is indeed "cornice." A cornice serves both functional and aesthetic purposes; it helps direct rainwater away from the walls and provides an attractive finish to the exterior of a building or room.

In architectural design, cornices can vary in style and materials, contributing to the overall character of a structure. They often enhance the visual appeal of door and window frames and provide a transition between the wall and the roofline.

The other options also have specific meanings within the context of construction and architecture. A frieze typically refers to a decorative band that can be found on the upper part of walls, often below a cornice, but does not specifically denote the trim above openings. A header is a structural component that supports the load above doors or windows, rather than a decorative feature. The soffit, located under the eaves of a roof, encloses the space between the roof overhang and the wall below, but does not serve the same decorative purpose as a cornice. Understanding these distinctions is important for recognizing architectural elements in home inspection.