I built a bridge across a river near my first home because of this. Add onto the fact that you can't swim down and pick up items in deep water and this became an absolute priority. No easy feat because building down into water is difficult.
I imagine for Breath of the Wild the teleported to nearest shore instead of a game over was thanks to beta testers who kept dying in bodies of water early in the game; so they fixed that.
People saying the water is freezing... not every water in the game is a river in the frozen wastelands. Sometimes it's just a pond. It's kinda ridiculous to die to that. Can't a fella just stop swimming and just float for a bit to catch his breath?
Never mind Zacsi's remark about how dangerous swimming in cold water is: With the year Angi is wearing it wouldn't work well in an indoor pool either :P
Can not ignore your swim skill. Raising it to about 7 will let you swim across the rivers.
Also as others have said you can keep moving while taking damage. If you DON'T move you can tread water forever with any amount of stamina left and wait for someone to rescue you in a boat.
You absolutely are able to keep swimming once your stamina runs out. My first time dying in that game was because I tried to swim a huge gap, and when I saw my health dropping (and regenerating at the same time thanks to a bunch of food) I just kept booking it in hopes I'd make it.
Most famous example of this is when the Titanic sank.
Though the first rescue ship got there within hour that was enough for most people to diem even though they could swim.
Sudden immersion into freezing water typically causes death within minutes, from cardiac arrest or incapacitation from cold.
It makes sense if you actually tried to ever swim in an enviroment of sub zero temperature. It's legit dangerous and a lot of people die doing it every year.
