Hello I work at the American History Museum in Concord MA. The Green Dragoons were called green because of the training program in South Wales or also known as Marland Uk. It was green because thats what the original uniform looked like when the training process began. there where also red,orange and blue Dragoons. They all wore red.
They were called green dragoons, and they wore red to impress the fact that the soldiers WERE British. The director thought that by using red they would be better identified as British by viewers. So although the historians pushed the directors to use green, they decided against it.
Tarletons (tavington) dragoons uniforms were green. He had an officers commission in the loyalst unit known as the green dragoons. Thier coats were fully green because at this time most loyalsts had green coats. On that note it is NOT trim they are facings!!!!!
Army's around the world help identify the different branches within the military by assigning them a color. Pre-modern uniforms (like those worn during the revolution) wore trim the color of there branch. Here's a break down of the Colors:
Blue= Infantry (foot soldiers)
Red= Artillery (Cannons, a.k.a. big guns)
Green= Dragoons (Heavy Calvary, main weapon was the saber)
Yellow= Calvary (Regular John Wayne type calvary, this was considered a small part of anyones main strategy, then during the Mexican-American war Dragoons were found to be obsolete and the Calvary to precedence, their main weapon is th carbine)
This is why their trim is differnt. It's to show their "specialty"