It seems to be late afternoon on a sunny day while trees are bare in the fall or spring. The camera is facing north. The trees on our left are probably in Central Park. I haven't identified the building on the right. It might be part of the Frick mansion at 70th St.
Here are a few close-up crops from the photo.
It's interesting that the horses are in the same pace. I've read that coach horses are supposed to use a mirror pace. The harness is spare — no girths, no saddles, no side straps, and no breeching straps around the horses' rumps to keep the cross stave from striking them on descents. Bad things will happen if the driver fails to slow the coach on descents by means of the foot brake which acts on the rear wheels.
This image shows the brake mechanism.
The guy who drives the coach is also its conductor and fare taker. The fare was a nickle. He would make change, but you might have to wait until his hands were free. He had to guide the horses and ring a bell as well as tend to passengers' needs. Though precariously high on what seems a pretty unstable vehicle, the top-side passengers appear relaxed and even a bit New-Yorkerly bored.
This is a dandy fellow on a handsome steed. Notice that he put the stirrups on the arches rather than on the balls of his feet. People went on foot or used coaches, cabs, and trolleys to get around Manhattan. They didn't ride horses on business; only for pleasure. I bet most people today would be surprised that an African-American might be out for a pleasure ride on tony Fifth Ave in 1900. Notice the dress and apron on the woman at right, a proper housemaid.
The building in the background is the old Lenox Library, founded by James Lenox at 5th Ave and 70th Street in 1871. Its collections, with those of John Jacob Astor, would form the nucleus of the New York Public Library. It was torn down in 1912 for what is now the Frick Museum and Library.
Fifth Avenue Coach Company Collection, Historical Note, The New-York Historical Society
Fifth Avenue Coach Company
Fifth Avenue Coach Company and Surface Transit on wikipedia
Harness on wikipedia
Coach Pair Dress/Show Harness
 Commenting on another 5th Avenue Coach photo, a person named TomVet says: "Whenever a team of two (horses or humans) is carrying or pulling a shared load they must be in step so far as stride and gait are concerned, but must be a mirror image or each will be fighting the other for control of the load. It's not at all the same as the "in step" we learned in the military for marching."
-- Perfectly in step TomVet on Mon, 07/26/2010 - 8:32pm.
 Parts of a harness:
Breeching ("britching") is a strap around the horse's haunches allowing it to set back and slow a vehicle, usually hooked to the shafts or pole of the vehicle. Harness saddle. A small supportive piece of the harness that lies on the horse's back (not the same as a riding saddle).
 The writer of a brief Sunday filler-piece in the New York Times on December 14, 1902, mentions the driver's fare-changing while describing a small attempt at flirtation: In a Fifth Avenue Stage, The New York Times MAGAZINE SUPPLEMENT, page SM16. The piece begins:
"Allow me, Madam," "Thank you." And the quarter is passed up to the driver -- no, not to the driver, but to the hole, where it remains tapping on the glass during the intervals when the hand is not engaged in ringing the bell.