Continuing north we come to the entrance at Reservoir and Sedgwick Avenues to Old Fort Four Park (its proper name according to the Parks Department website[1], but labeled as Fort Four Playground). It was opened in late 1934[2], some months before Strong Street Playground at the other end of Washington's Walk. Not the press releases, nor any other material I can find, give any credit to the New Deal for this park but since it was built in the same time frame on the same street as the Strong Street facility, and since the Parks Department is not thanking Mr. Rockefeller or other rich benefactor, and since Robert Moses' design and construction staff was entirely composed of “relief labor”[4], no other origin for this park seems plausible. Anyway, the issue of who to thank was a bit unclear in October 1934 because the CWA had been shut down six months earlier, and the WPA would not begin until five months later; other agencies such as FERA were picking up the slack in the interim on an ad-hoc basis. But by the time Strong Street was finished, the WPA was well-established and it is indeed acknowledged in the Strong Street Playground press release.

That leaves us with the question: who built Washington's Walk? Was it already there when Moses' workforce descended on this area in 1934-35?

In 1924 the City of New York commissioned the Fairchild Aerial Camera Corporation to produce detailed aerial photos of all five boroughs[5] that could be assembled into a giant map. The first image at left is of the Kingsbridge Heights / Bedford Park area of the Bronx, and second image zooms in on the Jerome Park Reservoir. Click the images to see them full size. You can also go to the NYPL site[5][6] or the NYC.GOV site[7] where tools are available to zoom even further. A close look at the Washington's Walk area reveals no signs of parklike features such as paths or terraces where they exist today. In fact, Webb Avenue didn't even reach Reservoir avenue in 1924, which is where the Washington Walk steps are.

So unless the Bronx Borough Parks Department or the Bronx Borough President built Washington's Walk between 1924 (when this photo was taken) and 1929 (when the Depression struck), then the entire stretch from the Strong Street Playground to Old Fort Four Park, including Washington's Walk and its paths, lighting, benches, trees, and overlooks, were one single project. Unfortunately Bronx Borough Parks Department reports are not available for 1924-29 (see list). However, close inspection of the Press Release for October 14, 1935[3] reveals a “new playground” opening at “Reservoir Avenue between University and Webb Avenues (Fort No.4)”. Although there is no playground there today, this is the precise location of a portion Washington's Walk, so we know it was created in 1935. Add to this the fact that Hugh S. Johnson, one of the architects of the New Deal, was present at the ceremony[3], and that WPA labor indisputably built the park a few feet to the south, and considering the facts laid out in Reference [4], the chances of Washington's Walk not being a New Deal creation are vanishingly small.

References:

1. Washington's Walk: Old Fort Four Park, New York City Department of Parks website.
2. New York City Parks Department press release of October 25, 1934: “The Department of Parks will open three more playgrounds on Sunday, October 28th, at 3:30 p.m. These playgrounds are located at ... and at Fort No. 4, Sedgwick and Reservoir Avenues, in the Bronx.”
3. New York City Parks Department press release of October 14, 1935: “The Department of Parks will open twelve new playgrounds throughout the city on Monday, October 14th at 4:00 P.M. Mayor La Guardia, Park Commissioner Robert Moses, General Hugh S. Johnson, Victor Ridder, Bronx Borough President James J. Lyons will speak at the opening of the Macomb's Dam Playground at Jerome and Sedgwick Avenues in the Bronx. Their speeches will be rebroadcast to the other playgrounds ... In the Bronx they are at Hunts Point and Spoffard Avenues and Faile Street; East 164th Street to Teasdale Place East of Boston Road; Reservoir Avenue between University and Webb Avenues (Fort No.4) and at Jerome and Sedgwick Avenues.”
4. New Deal Assistance in NYC Parks Department Projects, 1934-43.
5. Lionel Pincus and Princess Firyal Map Division, The New York Public Library: N.Y. City (Aerial Set) Section 1D, The New York Public Library Digital Collections (1924), labeled “City of New York, Board of Estimate and Apportionment, Office of the Chief Engineer, July 1, 1924,.”
6. Entire set of 1924 aerial views of NYC, NYPL, labeled “Only Public Domain”.
7. NYCityMap at GIS.NYC.GOV. Click where it says Map Type and then click "1924 Aerial". Then drag and zoom. The resolution is amazingly good.