There were other uniforms issued by the United States to the various branches of service and of course there were also the opposing Spanish forces with their uniforms for their branches of service.
There were the U.S. Marines, which actually had a campaign uniform very similar to the Rough Riders in that the Marine officers recognized that the canvas uniform was better for use in the tropics of Cuba. This image shows them in their more traditional wool uniforms.
And there was the regular army which stuck to its issue uniform of wool. The standard kit was a wool shirt, wool coat and blue wool trousers plus shorter leggings and a Mills belt. Many of the infantry were equipped with older model 45 70 black powder rifles from the 1870s as well.
The US Navy refined their uniforms from the wool of the Civil War to a cooler linen for tropical use but still had Dark Blue wool for dress and cooler climates
The Spanish also had a series of Uniforms for the branches of service. In Cuba, due to the tropical climate, they had cotton uniforms that were well suited to the terrain and the temperatures.