Hello. This was an interesting and enjoyable question.
The portrait is not as obscure as one might suppose. It was painted
by none other than Gilbert Stuart in 1806, and titled "Washington at
The best image of it I could find is here:
A bit of the story of how Stuart came to paint this painting is told
"In 1806, when Samuel Parkman proposed to give an unauthorized copy of
a Stuart portrait of Washington by William Winstanley to the city of
Boston for Faneuil Hall, public protests ensued, and Stuart was
persuaded to paint Washington at Dorchester Heights (1806, Museum of
Fine Arts, Boston)."
It's fitting, I suppose, that the painting hangs in a Boston museum,
as Dorchester Heights is just south of Boston, and was the scene of
one of General Washington's battles with the British in that eventful
Note that there are many copies of this painting done in oil and
hanging in many galleries and historical places -- whether the black
and white picture in the URL you gave is of the original or a copy is
impossible to say.
And why the particular pose of the horse? Only one of the sites I
visited offered some rather non-professional (from an art history
point of view) speculation:
"My favorite portrait of him is in Faneuil Hall in Boston. Gilbert
Stuart was the artist (at least that is what the tour guide said).
The portrait has Washington posing in front of a cannon and looking
into the past, with
his left hand squarely placed on the ass of the horse. Stuart was
clearly calling Washington a horse's ass."
I'd say it's unlikely, given Stuart's apparent reverence for our first
President. However, I should note that I had difficulty finding this
portrait until I ran a Google search on the terms: "George
Washington" "horse's ass".
I hope this is the information you need. I am posting an answer
quickly, as the information seems rather time-sensitive, but don't
hesitate to ask for follow-up if anything is in need of clarification