Request for clarity -- you've helpfully narrowed the time frame by specifying post-Marian. If you're referring to the late Republican/early Imperial time frame, the cavalry serving with a Roman army are likely to be composed primarily of auxiliary (foreign/non-Roman) troops hired by the Romans, so you do not appear to be interested in the older tradition of citizen cavalry making up the equestrian class and the "public horse" tradition. Does this sound more or less right?