I read on Reddit back then that whenever you take a horse out of a stable, its health is fully replenished. I used to think feeding them apples helped too but I think it only increases your bond level with them. How much damage they can take is determined by the strength stat, and is reflective of the weapon level they take damage from. So high damage weapons can be deadly if your horse is in a bad spot, that's why horseback combat can be particularly dangerous once stronger enemies start showing up with better weapons. I can't give exact values, but I can try digging for that thread I found on Reddit in March.
I've only had one horse die on me and it was shot by a bokoblin rider with one of the stronger lizal bows, so it basically died in two hits. Thankfully I was near the place where you can have a fallen horse brought back to life, so that's always an option if you get attached to a horse like I did haha. I won't spoil where it is, but it's out there!
