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One mother, Cyndi Stoddard, said she was frustrated the town did not propose another date for Halloween. She had to break the news to her 4-year-old daughter, who was planning to dress as a snow princess.

“My youngest is upset. She doesn’t understand,” Ms. Stoddard said. “I feel bad for the kids. It’s minor in the scheme of things, but it’s a big thing for kids.”

In New Jersey, several hundred children in Glen Rock gathered in the high school field and parking lot for “trunk-or-treat” Monday. There was an impromptu parade and children got candy by going from SUV to SUV in their costumes.

Some towns announced they were “rescheduling” Halloween.

The town of Somers, N.Y., about 40 miles north of Manhattan, announced it was moving the holiday, possibly to next Friday or Saturday. Town Supervisor Mary Beth Murphy said she’s received many calls from parents and “we’re not going to be ticketing 5-year-olds.”

The police department in the Hudson River city of Peekskill, N.Y., without prohibiting trick-or-treating, said in a news release: “It may be best that parents keep their children home and plan alternate activities with close friends and relatives rather than risk the hazards left in the wake of the recent storm.”

In Waterbury, Conn., Mayor Michael Jarjura asked city residents to postpone trick-or-treating until Saturday night because trees and power lines were down across the city and many neighborhoods were dark.

“We don’t want to usurp the role of parents, but this way here, a public declaration that we’re going to postpone it is more helpful to the parents and the residents,” Mr. Jarjura said.

Some parents were finding ways take their kids trick-or-treating, even if it was canceled in their hometown.

Doreen Kelley of Foxborough, Mass., said that when she heard the town had called off trick-or-treating, she decided to take her son to her friend’s neighborhood in Bellingham, about 20 minutes away.

“My son was disappointed, but I just called my friend, and we are going there, so he’s fine now,” Ms. Kelley said.

Associated Press writers Jim Fitzgerald in White Plains, N.Y.; Denise Lavoie in Boston; Rodrique Ngowi in Lexington, Mass.; and Dave Collins in Hartford contributed to this report.