In Colorado horses have the right of way always. everywhere. But I never tried to prove the point by crossing a busy street on my horse to see what would happen You can be technically right and very wrong all at the same time.
First of all, one doesn't
possess right-of-way. Others yield it.
But I don't believe there's anything legally that states what you are implying. In fact, for example, § 42-4-109.8 and § 42-4-109.13 of the
Colorado Revised Statutes state:
§ 42-4-109. Motorized bicycles, animals, skis, skates, and toy vehicles on highways
(8) Persons riding or leading animals on or along any highway shall ride or lead such animals on the left side of said highway, facing approaching traffic. This shall not apply to persons driving herds of animals along highways.
...
(13) Any person who violates any provision of this section commits a class B traffic infraction.
So it would seem that riding with traffic would be illegal.
But again, I am not a lawyer.