On New Year’s eve, a wave of sleet threatened to turn a densely packed Times Square into a particularly accurate facsimile of hell frozen over, with Mariah Carey’s performance providing the Luciferian soundtrack. But the hail halted well before midnight, allowing party-hoppers to search fruitlessly for cabs without mussing their hair. A refusal to be deterred characterized the week for many New Yorkers: Members of the Polar Bear Club hurled their untanned bodies into the frigid Atlantic. The footage pleased local news cameras nearly as much as the shots of NYPD and Coast Guard rescue crews scooping two involuntary Polar Bear Clubbers out of the Hudson after their small plane crashed. Mayor Bloomberg kicked off four! more!! years!!! with a vaguely inspiring and inspiringly vague vow to begin a national fight against gun interests and “rid our streets of guns,” while his West Side stadium sparring partner Christine Quinn was sworn in as City Council speaker, the first woman and the first openly gay council member in the position. The mayor could have promised to accomplish said crime-fighting by donning a cape and Batsuit, and he still would have been upstaged by Liza Minnelli’s rousing, lurching rendition of “New York, New York.” Liza took the song’s principle to heart; having made it here, she’s now looking elsewhere: “I’m writing a film!” she said, though she couldn’t recall the movie’s subject matter. Fake journalist Jon Stewart agreed to host the Oscars, while actual journalist Ted Koppel announced that he’s moving to the Discovery Channel. Hardly moving at all were the bedraggled passengers onboard Amtrak’s Silver Meteor train, which arrived in Penn Station more than 28 hours late from Orlando. But they made it in time to grab a final kosher sandwich at the 2nd Ave. Deli, which closed, at least temporarily, while owner Jack Lebewohl negotiated with his new landlord over jacked-up rent. But maybe his dues will decrease: An appraisers’ report documented a 20-odd percent drop in Manhattan real-estate sales. Sellers frowned, buyers smiled; Realtors shrugged, undeterred.