The phrase "a cozy atmosphere" is correct and usable in written English. You can use the phrase when you are describing a comfortable, home-like setting. For example: "The restaurant had a cozy atmosphere with warm lighting and inviting chairs.".
It was a cozy atmosphere of two-family homes.
Soft lighting, dark wood floors and cushioned seats create a cozy atmosphere.
Sarah Maxfield doesn't have to try hard to create a cozy atmosphere around her new work, "We deserve each other".
The flames were gas-generated, alas, but they lent a cozy atmosphere to the large loft dining room.
It's got a warm, cozy atmosphere, especially [for] a rainy day like today," Stronach said.
Incandescent bulbs are very popular because they produce a bright, warm light that helps with creating a comfortable, cozy atmosphere.
An excellent choice with a warm and cozy atmosphere.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com