Correct, if the statutes were to define a cyclist as an equestrian then the laws that apply to equestrians would apply to cyclists, unless otherwise stated. As far as where the law is silent, that is very unlikely in the US. By way of example, I cannot find anything that excludes my e-bike from the definition of a moped, which requires a license, in New Mexico. As a result of this, on my summer tour, which begins in about two weeks, I will not go through NM.