Here's why it's not a common noun:
* Common nouns refer to general things, like "cat", "tree", or "chair."
* Proper nouns refer to specific people, places, or things, like "John", "Paris", or "Facebook."
* "Warm and fuzzy" is a descriptive phrase, used to express a feeling. It's not a noun because it doesn't name anything.
You could use it to describe a noun, like "The warm and fuzzy feeling of a hug," but "warm and fuzzy" itself isn't a noun.