Hey, I'm 75% sure the episode in question is Scooby-Doo and the Invisible Madman, It was an episode from the What's New Scooby-Doo series and it takes place in a small snowy town. The villain is a character in an invisibility cloak and one of the suspects was a renowned Fashion Designer who Daphne is a f an of. She reveals to Daphne her new dress she is working on which follows a lumberjack theme I believe. I'm not sure whether it had fur but I'm sure it is the right episode.