It's common wisdom that wild mares live in a band with a single dominant stallion. However, mares have been observed leaving their herd to mate with the leader of a different band. Bands sometimes start because of a friendship between a single mare and a stallion that then attracts others. Breeding stallions may refuse to mate with specific mares (these days often, outside of the breeds that don't allow it, causing breeders to resort to AI). I once knew a stallion who would not mate with pinto mares, rather like a gentleman who prefers (or maybe does not prefer) blondes.
Although horses don't generally form the same kind of long term sexual bonds we do (their long term bonds tend to be platonic), they can form cross-sex friendships which might appear to be romances, and they can definitely decide to have nothing to do with a lover not of their choosing.