I only found one book which isn't a textbook named Storey's Illustrated Guide to 96 Horse Breeds of North America By Judith Dutson (not sure if it is good enough to follow) that defined these terms.
Outbreeding/ outcrossing is deliberately crossing one line of horse within a breed to a very distant or unrelated line. The term is also occasionally used as a synonym for crossbreeding.
Crossbreeding is the deliberate crossing of horses of different breeds.
Outbreeding or Outcrossing is the mating between two individuals of a breed but different varieties/sub-varieties.
Crossbreeding is the mating between two individuals of different breeds (could be intraspecific or interspecific as well).
Are these definitions correct?