Gum blankets were much more common and yes, ponchos were for cavalry. The Federal issue gum blankets had grommets and there are two specifically positioned where you can can string them together to wrap around yourself in the fashion of a poncho.
Here's a few photos of a correct reproduction of a Federal gum blanket, this one was made by L D Hanning. Notice the offset grommets in the one picture, those are used to make it a wrap around poncho. They can be used for a ground clothe or tied together to make a shelter. A very useful tool on both sides. When Southern boys could acquire one they held onto them.