As Hannah said, a purebred horse is a horse of one breed while a cross is of two or more. Crossbred horses are usually just referred to as both breeds (ex. Thoroughbred X Arab, or Shetland X Welsh). However in some cases some names have been developed to refer to specific breed mixes. An example of this would be the Welara Pony, a cross between a Welsh Pony and an Arabian.
A purebred horse is a horse of one breed. When two purebred horses of two different breeds mate they produce a crossbred horse, a horse of mixed breeds