warhorse vs riding horse

warhorse and riding horse both are nouns.

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

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

Other hypernyms of warhorse include mount, saddle horse.

warhorse (noun)	riding horse (noun)
horse used in war	a lightweight horse kept for riding only
a work of art (composition or drama) that is part of the standard repertory but has become hackneyed from much repetition
an experienced person who has been through many battles; someone who has given long service