It's my impression that horses don't see a lot of bikes and a quiet, fast thing coming up behind in their blind spot seems like a threat
I shout "bicycle overtaking" as soon as I am in shout range
I give them as much room as possible
I will slow up usually. Sometimes this doesn't work, if it would mean applying squeaky brakes then probably the horse wouldn't like that
I always say "hello hoss" to the horse. And sometimes "good afternoon" to the riders
Despite all this, on numerous occasions I've had grief from posh, clueless fuckers. The rule that there are idiots on the road regardless of what they are on (bike, car, van, horse) holds true.
A skittish horse isn't too blame, the rider is. The rider is on a horse they can't really control in traffic
Most stupid comment from horse rider: "you shouldn't wear hi viz, it scares my horse"