While the "nose muffs" appear to be simple nose clips, a close look shows that they are shaped like tiny earmuffs.
When Cornflake S. Pecially suggests to Lady Aberlin in. Taking the excess garbage to Westwood, he reminds her, "We got together with them about the community pool." This is in reference to episode 1530 where Mayor Maggie and Mr. Aber made a proposal about building a swimming pool in Make-Believe.