Yes; that is the correct spelling of "galloping horse".
correct spelling is thoroughbred, and that is a broad question. Depends on the type of riding and the horse.
That is the correct spelling of the plural noun "horses."
That is the correct spelling of "Hanoverian" (a horse breed).
Neighed is the correct spelling. (cry of a horse)
Le cheval, les chevaux.
That is the correct spelling of "seahorse" (a fish with a horse-like head that swims erect).
His name was Babecia (sorry about the spelling) .
That is the correct spelling of "carriage" (originally a horse-drawn conveyance).
That is the correct spelling of the proper noun (breed of horse) Appaloosa.
That is the correct spelling of "stretch" (to elongate, or the final part of a horse race).
The correct spelling is "charley horse" for muscle cramps. It refers to a painful muscle spasm or cramp that typically occurs in the leg.