Cavalry was used throughout the war. Horses were ubiquitously used to pull loads. In Sam Fuller's "The Big Red One" there's a WWI scene at the beginning which has a horse, not gonna post spoiler details, but that scene is based on real experiences. However, as we know, Hollywood doesn't make documentaries.
In the Second World War, the Germans used horses to pull artillery and logistics for their non-motorized/mechanized divisions.