According to the Oklahoma Cooperative Extension Service, sheep do drink from running water. In fact, they prefer moving water to still water. For food, sheep prefer to graze pastures, eating hay, timothy, weeds and other vegetation, Barking Rock Farm indicates.
If pasture options are poor, sheep are sometimes given commercial grain feed designed for the animals' specific nutritional needs. These mixes often contain corn, soybeans, oats, peanuts and alfalfa pellets. It is also common practice to provide sheep with salt blocks or loose mineral salt. Because of this, it is essential that sheep have access to fresh, clean drinking water, whether or not it is running.