It's actually not well understood that most
liberal horses do not in fact let any
human or other
creature ride them. Liberal horses, being the
bleeding hearts that they are, are against
animal cruelty, and
subjugating an animal for the express purpose of being the
conveyance of another animal is tantamount to
slavery. So, indeed, the myth of liberal horses being rode is exactly that, a
myth.
Also, the idea of having sexual intercourse with any horse would also be anathema to the liberal horse philosophy. Yes, your liberal horse would be free range, chewing on organic alfalfa hay and oats, and engaged in peaceful, yet effective environmental action.