[Minor edits 12/25/09; 4/13/10]
The British Legion was formed at New York in 1778 from other Provincial units. The term "legion" refers to the fact that the regiment included both an infantry and a cavalry component (specifically, "dragoons"). The Legion also apparently had a band, and, according to Colonel Otho Williams, their instruments were captured at the battle of Cowpens.
The infantry of the Legion usually fought on foot, but detachments were sometimes mounted, most notably at Waxhaws and Hanging Rock. Some of the Legion infantry were apparantly mounted at Cowpens, too, for Tarleton commented that "the cavalry and mounted infantry brought up the rear" during his approach to the battlefield.
The British Legion was one of the most active units during the later years of the war. The regiment (or detachments thereof) saw action at Indian Field in 1778, the siege of Charleston, Lenud's Ferry, Monck's Corner, and Waxhaws in the Spring of 1780, Williamson's Plantation, Rocky Mount, Hanging Rock, Camden, and Fishing Creek in the Summer of 1780, Fishdam Ford, and Blackstock's Plantation in the Fall of 1780, and Cowpens, Torrence's Tavern, Wetzell's Mill , Guilford Courthouse, and Yorktown in 1781.
The many battles in which this regiment participated took a severe toll on the rank and file. Loyalist Alexander Chesney wrote that at the time of Cowpens, the dragoon companies were "filled up from the prisoners taken at the battle of Camden."
The uniform of the dragoons is well documented as short green jackets with black cuffs and collars (see especially this famous painting and Don Troiaini's modern one). The recollections of Cornet James Simons of the American 3rd light dragoons confirmed that this uniform was worn at Cowpens, “Colo. Tarleton's Legeonary Cavalry... wore a Uniform of Green with black facings.” The infantry of the Legion probably wore green jackets as well, although the "Barron Map" of the Battle of Camden shows them in red coats with black facings.
Philip R. N. Katcher (1973). Encyclopedia of British, Provincial, and German Army Units 1775-1783. Stackpole Books.
Johann Ewald (1979). Diary of the American War: A Hessian Journal. Translated by Joseph P Tustin. New Haven: Yale University Press.
Lawrence Babits. (1998). A Devil of a Whipping: The Battle of Cowpens (amazon.com link).
The Journal of Alexander Chesney is available here through Google Books.
A summary of the Otho Williams papers can be found here. The item in question is a letter from Williams to Dr. James McHenry, dated January 23, 1781.
Marg Baskin's Banastre Tarleton website is a fantastic resource for Banastre Tarleton and British Legion aficionados.