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.