riding horse vs saddle horse

riding horse and saddle horse both are nouns.

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

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

Other synonyms of riding horse include mount.

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