I'm going to continue to approach slowly, talking to the horse/rider then either ride slowly by or dismount and walk depending on instructions from the rider/signs from the horse. I'll even remove the helmet/glasses (if dismounted) and keep talking when that's what it takes.
Share the road does not only apply to cars, it means us, too, to cars, horses, joggers, whatever. Not stopping a paceline because of the inconvenience sounds familiar...only insert 'car' for paceline and make the inconvenience 'bike' instead of 'horse'.
I wouldn't want to be responsible for another being's misfortune.
(1500 pound rabbit....I love it....If I'm ever fortunate enough to have a horse I'll have to call him Harvey!)
I used to have an open mind but my brains kept falling out.