cow pony vs saddle horse

cow pony and saddle horse both are nouns.

Word	Noun	Adjective	Verb	Adverb
cow pony	Yes	No	No	No
saddle horse	Yes	No	No	No

As nouns, saddle horse is a hypernym of cow pony; that is, saddle horse is a word with a broader meaning than cow pony:

Other hypernyms of cow pony include mount, riding horse.

cow pony (noun)	saddle horse (noun)
a light saddle horse trained for herding cattle	a lightweight horse kept for riding only