For some reason, when riding horses, fall distance isn't canceled when touching the ground after a one block drop, and the horse continues to accumulate fall distance until you dismount, whereupon it takes the entire accumulated distance's worth of fall damage in a single hit, usually killing the horse instantly. This has cost me several horses so far. The reason I know this is the case is that dismounting while in 2-block deep water is the only way to stop the horse from dying when you dismount, and sometimes after dismounting I've taken fall damage too.
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I know this is listed as duplicate but it is the best detailed description of the problem. I was testing speed for various horses and had no damage dismounting. Once I took a horse out of the relatively flat plains then it took MAJOR damage dismounting. I was also going through trees but the elevation change makes much more sense.
Duplicate of MC-96583