NEW YORK — With many residents left homeless after the devastation from last week’s storm, New York-area officials began focusing Sunday on another factor that might make the problems even worse: colder weather that is moving into the region.

In New York, 20,000 to 40,000 people, many of them residents of public housing, will have to find homes, Mayor Michael R. Bloomberg said Sunday. Earlier in the day, Bloomberg compared it to the situation after Hurricane Katrina in New Orleans but later seemed to temper his assessment after news that power had begun to flow in some of the hardest-hit regions.