Neither snow nor rain nor heat nor gloom of night might keep them from their appointed rounds — but these thieves will.

Manhattan postal workers are being terrorized by brazen bandits who don fake uniforms and work in teams to swipe their carts, police sources told The Post. At least 19 mail carts have been stolen in Union Square, Murray Hill and the Upper East Side since summer, according to sources.

“It’s easier to steal a mail cart with a significant amount of mail than sticking a glue trap in a mail box,” a law-enforcement source noted.

In the latest case, on March 15, a robber wearing a fake postal jacket waited for a female carrier to leave her cart outside 136 E. 36th St. while she delivered mail inside. Once the mail carrier was out of sight, the thief ran off with the cart. He was caught on video running east on 36th Street.

The thieves rifle through the carts’ mail for valuables such as money orders, checks and credit cards, and then ditch the rest.

Police are now investigating two patterns of mail theft in Manhattan occurring north and south of 59th Street, according to sources.

Eight incidents north of 59th Street have been reported between Aug. 30 and Dec. 1, including one on Oct. 17 in front of 223 E. 78th St. A witness saw that robbery go down after the mailman went inside the building.

“Some guy just passed by and took his cart,” the bystander said. “At first, I thought it was a joke. I thought the guy knew the mailman.

“Then there was one guy 10 feet in front of him leading the way, basically making sure the coast was clear,” the witness recalled.

There were 11 incidents south of 59th Street between Oct. 2 and March 15, including two nearly back to back and around the corner from each other: One occurred on Jan. 26 in front of 18 E. 16th St. and the other four days later at 140 E. 17th St., sources said.

Only one person has been arrested in the thefts so far.

A male postal worker chased down Rasul Salaam after he was caught walking down the block with a full mail cart he had just lifted from outside 249 E. 77th St. on Nov. 10, according to sources and a criminal complaint.

Salaam, 29, pleaded guilty to criminal possession of stolen property and received a 60-day jail sentence.

A postal worker who was recently delivering mail on the same block — and who left her cart outside some of the buildings — said it is not always possible to bring her cart indoors.

“Some buildings, the doorman doesn’t want it inside,” she said.