I have a moss-like fungus on the "tree" portion of my rose bushes - crepe myrtles and even my peach tree. I am in Florida, so it gets very hot here.
My guess would be downy mildew: https://www.gardeningknowhow.com/plant-problems/disease/downy-mildew.htm
In order to be absolutely sure, you can take some samples to the county extension service for analysis. This link will help you locate the nearest one: https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm