“We have the opportunity to show the world how Cortina is beautiful in a different way,” said Manuel D’Avanzo, the owner of the VIP Club, which he called “a holy grail” for wealthy, night-life loving Italians. It is a place, he said, with heritage and history — and now a sponsorship deal with Rolls-Royce. At least one sliding-sport athlete admitted to slipping out with teammates to party at the club during the Games, though he was granted anonymity when he pleaded that without it, he would be thrown off the team. (“Our coach will kill us,” he said.) Mr. D’Avanzo agreed that it was more prudent for athletes to come after they won their competitions, “not before.”