Another thing I missed on that part was to check the horses speed stats. I didn’t realize you could do this before mounting the horse. It seems the middle horse (the one with a name) is the fastest ride of the lot. The other horses seem to be random ones generated by the game for the Cumin NPCs.
So I’m betting that named horse is the one the castle guards told you to ride…before slamming the portcullis shut in your face