I spotted this meme on social media and quickly determined that it wasn’t in fact a tribute to the many horses killed in the First World War. On looking further I found this excellent post that means I don’t really need to add much. The gist is that it’s one of a series of photos in this style, and this one commemorates one officer’s (the CO of the ‘remount’ unit in question) horse; that of Major Frank G Brewer. It was taken in 1919, not 1916 (the U.S. hadn’t even joined the war at that point) and although it’s possible that Brewer’s horse was killed in the war, it’s equally possible (if not more likely given that he was CO of a non-front line unit) that it died of old age – or that it wasn’t, in fact, dead at all (the caption does not suggest this). No-one’s been able to determine those facts (and I have attempted a search myself), but regardless, it certainly isn’t a tribute to the dead horses of the conflict. Animal rights hadn’t quite reached that point in 1919, sadly. Most horses were seen as tools and property, although of course individuals had strong relationships with them as they do today.
All I can add to the linked article is that the original image is available in high resolution on the U.S. Library of Congress site.