American Truck Simulator doesn’t have too much in the way of weather, other than rain. You also have the different times of day, but the only thing it changes is whether you need your headlights on. While there isn’t a mod that adds a wide variety of weather yet, the Foggy Weather mod adds something extra to the game.
The weather can become slightly foggy in the desert, as well as around some parts of the Pacific coast. There is also a chance of encountering a sandstorm further in-land. Depending on your route, the change of weather might make your journey more interesting.