cow pony vs riding horse

cow pony and riding horse both are nouns.

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

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

Other hypernyms of cow pony include mount, saddle horse.

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