saddle horse vs riding horse

saddle horse and riding horse both are nouns.

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

As nouns, saddle horse and riding horse are synonyms defined as:

Other synonyms of saddle horse include mount.

saddle horse (noun)	riding horse (noun)
a lightweight horse kept for riding only	a lightweight horse kept for riding only