If you still plan on finishing this mod I have some research that I'm sure could be useful to you
American cavalry is basically going to be all light dragoons and perhaps a volunteer cavalry regiment. In January of 1812 with the war eminent, congress approved the creation of a second light dragoon regiment, the 1st and 2nd Regiment of United States Dragoons. And in 1813 Richard Mentor Johnson raised two battalions of volunteer cavalry, roughly 1200 men divided into 14 companies. These volunteer cavalrymen earned some fame for clashing with the British 45th Foot and prevailing.
Armament of American dragoons: carbine (I'll find out what model), 1796 light cavalry saber
Armament of American volunteer cavalry: long rifle, random melee (knives, sabers, tomahawks, etc)