For a quick cleaning solution without getting the hoses and buckets out, try a dry shampoo.
Things to Consider:
Injuries/Bandages -- For areas that need to stay clear of water, a dry shampoo can help you still clean your horse and avoid excessive contact with water.
Healthy Coat -- Keeping your horse clean will create a nice shiny coat and often help with dry skin conditions.
Brush First -- Be sure to do a thorough brushing first to remove all dirt and manure before you apply dry shampoos.