How to write a scene where you're slowly freezing to death?

Curious, you absolutely have to do the research. Marli's advice is, as usual, solid. I strongly advise following it for what happens to your character physically.

I'd also advise reading accounts of people who had similar experiences but lived. My understanding is incomplete, since I've never researched it, but it's supposed to be not all that bad.

Only you, of course, know your character well enough to guess how he will react to both the physical aspects as well as his rapidly approaching death. Some people would be stoic, others hysterical. He might easily go through the seven stages of grief.

Google "hypothermia symptoms"?

Perhaps there are descriptions in books about or by explorers of the Arctic and Antarctic; survivors of the Titanic sinking; and mountain climbers.

Harry Houdini did escape stunts where he was shackled and lowered into lakes and rivers.

The best thing to do is to rely on personal experience. Go out with a friend somewhere, and put yourself into a situation of extreme cold. Your friend can help you warm up. There's nothing like personal experience for writing.