Walking horse vs riding horse

Walking horse and riding horse both are nouns.

Word	Noun	Adjective	Verb	Adverb
Walking horse	Yes	No	No	No
riding horse	Yes	No	No	No

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

Walking horse: a horse marked by stamina and trained to move at a fast running walk
riding horse: a lightweight horse kept for riding only

Other hypernyms of Walking horse include mount, saddle horse.

Walking horse (noun)	riding horse (noun)
a horse marked by stamina and trained to move at a fast running walk	a lightweight horse kept for riding only