I only lost one horse so far. I was driving a train and the horse was following along. But it seems that it couldn't bear to be replaced and in a fit of depression dove under the trains wheels. Instant death, no chance to revive.
I picked up my saddle, placed it on the train and drove to a station close to a stable. Then manually carried it to the nearest stable . It was quite a hike and I tried begging for a ride from passing carts, some of their comments nearly made me just shoot them and steal a #%&*$# ride.

I finally moved on to Chapter 3, mostly to unlock some more equipment to get some of the different challenges completed.