TL:DR - last line.
The Fandom article Cloak of Invisibility (under Behind the Scenes) provides some relevant information. It may be unreliable, but let me elaborate.
Many things could detect people who were using the Cloak, as we see in the series, such as the eye that Moody possesses and the Marauder's Map. Now, the last bit sounds interesting.
It was also unable to hide Harry from creatures able to sense location by methods other than primarily sight, such as Dementors and Nagini.
Animals that use senses to roam could be able to see under the Cloak (possibly echo location, and snakes).
Dementors can as well, which may lead to snakes being able to.
"Dementors can’t see, you know. . . .” He swallowed. “They feel their way toward people by feeding off their emotions" — Sirius
Emotions such as fear can be sensed by Dementors — if you possess fear, they may be able to know where you are due to this, Cloak or not. As it only protects the user from some spells and sight, I'd assume the latter is correct.
Although different, Mrs. Norris and Crookshanks may have sensed the presence under the the Cloak as well.
As Dementors can sense people under Cloaks via fear, it reinforces the statement that snakes can sense anyone under the Cloak via smell, and possibly heat.