It isn't necessarily a sheet per se as you would think of something like a stable or turnout sheet. A cooler is usually made of wool, or some other material, that helps wick away any moisture, such as after bathing, heavy work etc, and keeps the horse warm while they are drying.
Some coolers do have the shape and fastenings like a regular sheet but are not meant to be worn such as overnight etc. Other types of coolers will cover the entire horse from poll to tail and about halfway down the legs.
Here are some cooler versions: Dover Saddlery - Search Results for cooler