Exact same thing brought me here. Used my DLC code for the War Horse. Finished the hunting mission so I could use the War Horse. Fed her. Bonded with her. Named her. Brushed her. All good.
Then I'm on foot next to a departing train and think "I wonder what happens if I hitch a ride without a ticket? Cool, it's a crime! And Morningstar (my beloved War Horse) is running alongside! Man, Rockstar really thought of everyth.....oh...she hit rocks and went under the train..and I'm being shot at..and now I'm dead...cool"
Anyway. I come back, whistle and get some brown nag. Huh. Ride the nag to the stable aaaaaand no more Morningstar. I have two Tennessee Ranchers and the brown heap of glue I rode in on.
I never had this much trouble with Dogmeat.