The day before, bathe the horse. Make sure you do not use an oil based shampoo or conditioner, as this attracts dust. Spray the horse with a coat dressing such as showsheen, thi coats the hair with silicone,making dust rise to the surface. Where it can be easily brushed off.
When you are preparing for your class, be sure not to use products such as baby oil, as they attract dust. Your horse should be clean enough that you can use a baby wipe to collect any dust that has rosen to the surface. There are ways to prevent getting the dust on your horse, but, horses will be horses and they will find a way to get dirty/