Do horse riders have the right-of-way at a highway crossing?
Generally speaking, no, because the Vehicle and Traffic Law (V&T § 1261) treats horses as vehicles. It doesn’t matter if the rider is leading the horse or in the saddle. The requirement to yield to pedestrians does NOT apply to horses.
Drivers always need to be careful around horses. Also, § 1146-a, applies to horses on the road, not those crossing a highway. The V&T Law does say someone riding a horse must come to “a full stop before entering the roadway.” (V&T § 1262)
For a mid-block crossing, a yellow and black horse crossing sign would not give the horse rider the right-of-way. The proper traffic control device for halting traffic for a horse rider in a mid-block crossing would be a pedestrian hybrid beacon (https://mutcd.fhwa.dot.gov/htm/2009r1r2/part4/part4f.htm).
Vehicle and Traffic
§ 1261. Traffic laws apply to persons riding or leading horses. Every person riding or leading a horse upon a roadway shall be granted all rights and shall be subject to all the duties applicable to the driver of a vehicle by this title, except as to special regulations in this article and except as to those provisions of this title which by their nature can have no application.
A horse is counted as a vehicle which means at a crossing, a car would have the right of way unless there is a traffic control device instructing the car to stop. The requirement to yield to pedestrians does NOT apply to horses.
Note the following V&T law section regarding horses:
§ 1146-a. Approaching horses.
1. Notwithstanding the provisions of any other law to the contrary, every driver of a vehicle shall exercise due care to avoid colliding with any horse being ridden or led along a public highway.
2. Every driver of a vehicle shall approach a horse being ridden or led along a public highway at a reasonable and prudent speed so as to avoid frightening such horse and shall pass the horse at a reasonable distance.
3. No driver of a vehicle shall sound the horn when approaching or passing a horse on a public highway.
It is also important to for drivers to be aware of their speed before and after they pass a horse and rider. Many drivers politely slow down and give the horse a wide berth, but as soon as they pass the horse, they “gun it” which often spooks the horse more than if the car had been at a steady pace the whole time.