You mean we have American Lighthorsemen? Way Cool!!
How do you know they'll dismount to fight? Most of the time they probably will, but maybe not always. I've seen pictures of Chinese or Mongolian troopers riding very similiar horses, full gallop and firing an AK in full auto. A Double Dose of Rock n Roll, as it were.
Fighting afoot would technically make them Dragoons, although historically, especially in America, Dragoons often fought mounted and Calvary sometimes fought afoot, blurring the distinction.
Some were reported yesterday to be leading a charge on Taliban positions on horseback. I call that a Calvary charge.