Walking horse vs saddle horse

Walking horse and saddle horse both are nouns.

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

As nouns, saddle horse is a hypernym of Walking horse; that is, saddle 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
saddle horse: a lightweight horse kept for riding only

Other hypernyms of Walking horse include mount, riding horse.

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