* Cosy implies a sense of comfort and warmth, often associated with a feeling of closeness and intimacy. It can also describe a place that's small and inviting. Think of a cozy cabin in the woods or a cozy armchair by the fireplace.
* Snug implies a sense of tightness and security, often associated with feeling safe and protected. It can also describe something that fits well and comfortably. Think of a snug blanket on a cold night or a snug fit for a pair of shoes.
So, in short:
* Cosy is more about feeling comfortable and relaxed.
* Snug is more about feeling secure and protected.
They can overlap, but there's a subtle difference in their meaning.