Definitions of cozy:

• noun:   a padded cloth covering to keep a teapot warm
• adjective:   suggesting connivance

  Example: "A cozy arrangement with the police"

• adjective:   enjoying or affording comforting warmth and shelter especially in a small space

  Example: "A cozy nook near the fire"

• adjective:   having or fostering a warm or friendly atmosphere; especially through smallness and informality

  Example: "Had a cozy chat"