Some P&C can sustain a cozy atmosphere even with some moderately heavy themes or light comedy. However, it depends a lot on the game. For instance, I would not consider The Longest Journey cozy, even though it is one of my favorite adventure games. Nor my absolute favorite, the Blackwell series.

But I would definitely consider Monkey Island, Broken Sword and Kathy Rain cozy. Why? It is very hard for me to articulate. Besides the obvious (beautiful graphics and sound that is not too "challenging") it is something about the narrative working in a well-defined sandbox without too many surprises, but not in absolute monotony either. And the plot and story not being too heavy, while not being a complete farce either.