The four men were seen appearing to harass some of the more than 100 animals inside the Sweetbriar Nature Center in Smithtown.
"I am furious and disgusted," Sweetbriar Director Janine Bendicksen told WCBS-TV. "They harassed them. They were here causing trouble."
The men, in hoodies, climbed into a pig pen, opened cages and disturbed the animals inside, authorities said. They allegedly gave beer to a goat and were captured on video laughing about it.
When the suspects discovered they were being recorded, they grabbed the security camera and threw it in a nearby pond on the property, the Smithtown Department of Public Safety said.
Authorities discovered the camera last week during a routine water quality inspection.
The men could face animal cruelty and criminal mischief charges.