Here's a bit of trivia on the 1st Cav patch from the Cavalry Times.
"When, in September of 1921, a new unit designated 'The 1st Cavalry Division' was authorized, the question of an identifying insignia immediately arose. The prevelant regulations dictated the insignia would have three principles: 1. Bind men together in a common devotion; 2. To be an easily recognizable sign around which men could reassemble after battle; and 3. Be a word picture which would bring inspiration to the hearts and minds of the men of the division. Due to the economic restrictions, the patch should be composed of only two colors.
"The unit was stationed at Fort Bliss, Texas, where the sand and dust never settles, and where also was stationed Colonel and Mrs. Ben Dorcy. It seems that they were well known for their knowledge of heraldry and decided to design an insignia for the new division. They agreed that the traditional cavalry colors of blue and gold would be a good color for the background of the new insignia. It so happened at that time that Mr. Dorcy was cutting up an old dress blue cape of her busband's which had a bright yellow lining. This became the cloth upon which the first patch was drawn. Seeing a trooper ride by mounted on a beautiful black thoroughbred horse, it was immediately decided to use the horse's head in the design.
"They then chose the shape of a Norman knight's shield for the outline of the patch. It was customary in medieval times for the knights to have their family coat of arms painted on their shields. Since few people could read, troops could rally around the knight's emblem during battle. It therefore became a noble and symbolic choice for the new patch design. The bend (stripe) across the patch also came from heraldry. It is to represent the scaling ladders used in ancient battles to breach the walls of a castle. It occupies a place of honor equal to the horse because both were necessary to meet and defeat the enemy.
"Colonel Dorcy then finished sketching the design on the yellow cape lining, Mrs. Dorcy sewed on the bend and the design was accepted as the 'First Team's' symbol. It was the largest patch in the Army and its size was justified by being at Fort Bliss, where the swirling dust often obscured smaller designs.
"It is designed so that, when worn on the left shoulder, the horse faces the enemy. And when worn on the right shoulder, the horse is facing the rear, remembering service and accomplishments in the past. Today, the original patch resides in the library of the US Army War College in Carlisle Barracks, PA."
Both of you guys nailed it. Within three hours, too.
I have to give Stonewall Jackson the palm for the most complete answer, and PAR35 a prize for the cleverest one.