“Cold feet” is an idiomatic expression. It means last minute fear that one feels before taking a planned action. “Fuzzy slippers” is meant literally — slippers that are covered in “fuzz” — the fuzz helps them keep your feet warm. The speaker is telling the other person that he / she is just experiencing last-minute jitters, and that ignoring the fear is as easy as putting on slippers. The joke is based on interpreting the expression “cold feet” literally.

Slippers are a type of shoe that you can slide your feet into, oftentimes with no heel part. In America the shoes are usually used in the morning and at nighttime but in some parts of the world can be used for guests, etc.