Cozy, in the context of a warm beverage cover, refers to a soft and snug item, typically made of fabric or similar material, that is used to keep a hot drink, such as a cup of coffee or tea, warm for a longer period of time. It is often decorative and provides insulation to help maintain the temperature of the beverage.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: Warm beverage cover. Explanations are generated by AI and may be inaccurate.