saddle horse

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun A horse bred or trained for riding.

from The Century Dictionary.

• noun A horse used with a saddle for riding.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A horse that has been specially trained for riding, specifically the American Saddlebred.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a lightweight horse kept for riding only