I have pretty much read this thread from end to end, and told myself over and over not to reply.... but I just can't help myself.
There is a local group of cyclists who, every year, do a fancy dress ride for charity. The other day, while riding my horse I encountered several cycle mounted characters from Star Wars. A couple of years ago I came across a large group of cycling Elvis impersonators and we have also had Arab terrorists, complete with vests covered in dynamite.
On every occasion my horse has reacted the same way, or more accurately, failed to react at all.
On another occasion we were passed, on the road, by a large group of riders on mtb's, again, no reaction, other than to investigate if any of them had anything tasty to eat. An hour later, when I was on a particularly steep and rocky climb, I met the mtb'ers again, only they were now coming down! The riders were excellent and called back to warn others in the group and I rode my horse as far off the track as possible which was fine by him, as there was some yummy grass there.
The point I'm making as a horseman, is that not all horses are potential unexploded bombs and they don't all spook at the drop of a hat. It also has a LOT to do with the horses rider, and here is where most of the problem lies.
As a cyclist, I often come across horse riders on the quiet country roads I use, for this reason I have fitted a bell to my training bike, a quick PING lets both horse and rider know you are there, and a few words exchanged will sort out if the horse is nervous or not. If it is, I talk to the horse as I go past.
I have met lots of horses as a cyclist and lots of cyclists as a horseman, I've never had any trouble in either role due to consideration from both parties.