Why does hypothermia kill us?

There's this thing about temperature and molecules. The higher the temperature, the faster molecules go. That's how ice melts into water, and then evaporates. It's also how earth becomes magma. In the same sense, colder temperatures slow down these molecules-- things solidify and crystalize. In the same sense, our bodies, when our temperature drops, are slowing down. Things in our body stop working. The heart rate and blood pressure continues to drop as the rest of the body is pausing too. While this is happening, you would become more fatigued, thus the temptation to "just lay down and rest for a bit". Heat provides the warmth we need so this doesn't happen.

All proteins and enzymes have evolved to work optimally at certain temperatures. In us, they work best around our normal body temperature. If you heat up to much they stop working, same is if the temperature gets too cold.

Cold affects mostly our brain and other nerve cells. Pace maker cells for the heart slow down, so heart beat is slow and possibly irregular. If it stops, you end up dead.

At core temperatures less than 33°C, brain electrical activity becomes abnormal; between 19°C and 20°C, an electroencephalogram (EEG) may appear consistent with brain death. Basically your brain stops working. If your brain stops to tell you to breathe, you die.