The plunge here belongs to a building rather than a yard. These are bathhouses with chilled pools, steam rooms and ice rooms, so the cold is engineered rather than borrowed.
Brooklyn and Manhattan split the bulk of it, and the cut reaches out through Queens to the Jersey suburbs. Many run aufguss on a schedule and serve food, so a session turns into an afternoon.
In the NYC Metro, 11 of the curated saunas fit this cut. See the full the NYC Metro region guide for every venue, or keep scrolling for just the saunas with a cold plunge.
Every sauna with a cold plunge in NYC Metro

Bathhouse Atlantic Ave
$$Brooklyn, United States

Bathhouse Flatiron
$$New York, United States

Bathhouse Williamsburg
$$Brooklyn, United States

Brooklyn Banya
$$$Brooklyn, United States

Brooklyn Bathhouse
$$$Brooklyn, United States

Island Spa & Sauna
$$Edison, United States

New York Spa & Sauna
$$New York, United States

QC Spa New York
$$$New York, United States

Russian & Turkish Baths
$$New York, United States

Spa Castle
$$$Queens, United States

World Spa
$$$Brooklyn, United States