History of the park as detailed by the Woodland Park Zoo is available online at http://www.zoo.org/about/chronologicalhistory and below.

1914: On January 23rd, the southwest corner of WPZ, later known as the War Garden, was dedicated to the veterans of the Spanish-American War. Two Civil War-era barge howitzers (small wheeled field pieces) were added to the existing naval guns that had been placed there in 1911. A plaque made of metal from the USS Maine was set there as well, to honor the personnel of the USS Illinois. It is not clear why the Illinois was specifically honored.

1924: A statue, “The Hiker,” portraying a Spanish-American infantryman, was placed in the War garden (the southwest corner of the park near N. 50th St. and Phinney Ave. N.)

From The SunBreak:

The SunBreak does a great job of detailing the history of each piece of war memorabilia located in the park, including the plaques shown below. Access the story here: http://thesunbreak.com/2013/06/08/7-odd-things-to-see-in-seattle-parks-north-end-edition/7 or Odd Things to See in Seattle Parks (North End Edition) – The SunBreak, created using web.archive.org.

From HistoryLink:

Learn more about Seattle’s connection to the Spanish-American War from HistoryLink.org.

1. First Washington Volunteer Infantry Regiment Muster for the Spanish-American War on May 1, 1898: http://historylink.org/File/5526
2. Spanish-American War Volunteers return to Seattle on November 6, 1899: http://www.historylink.org/File/2051