Hello,
As a fellow mule owner..... the reactions you have described from people is just due them being prejudiced, (and I don't mean that nastily at all) - they were probably genuinely worried that horses may be worried by/scared of your mule and envisaged large heaps of earth-bound riders being unsteated by spooked "short ears".
As you will hopefully have discovered, it would not have taken very long to see that whilst horses are often mesmerised by mules, they just don't seem to be afraid of them. (I am sure there will always be exceptions, of course, but then there are horses who go nuts at the sound of a rustling waterproof)
The staff at the livery yard I use, and I think my trainer, and in fact me too, were all a little worried when I first imported my mule, as to what the horses would think when they saw their first mule. We needn't have been concerned - so far, without exception (she has now met in excess of 70 horses in the UK) not one has been afraid, about two thirds have been very curious indeed, and a handful have been totally obsessed, calling and gawping at her. Including my QH, which was very funny, who seems to forget he is in fact a gelding and gets hugely excited when he sees her.
So yes, horses DO know there is something a bit different about mules; some horses ARE afraid of donkeys, and it is a perfectly natural concern for people who are aware of this to be a little concerned about how horses might react to their first mule (perhaps the organisers of the fun ride may have been worrying about their insurance premiums if every horse spooked at the mule, not realising that wasn't likely to happen at all).
Now that saddle mules are so rare in the UK, so is mule experience.
So, it is up to people like you - and me when mine is ready to go out in public (she's only just had her 3rd birthday so will be a while) - and Laura, also on this forum, and has a saddle mule that competes, and jinglejoys, who has a Spanish import she is now riding, and anyone else lurking with a mule hidden away - to be sensitive to people's perfectly valid initial concerns; reassure them that, although reasonable, those fears are in fact unfounded, because even known donkey-phobic horses don't seem to have a problem with mules... and get them out into the public arena and show them off.
Word will soon spread that actually, a mule doesn't upset the horses, and hopefully as there used to be a well-known mule competing at WES shows a few years ago (sadly the owner has now passed away and I never got to meet her) you will find more automatic acceptance of your mule amongst western riding circles.
Good luck and best wishes, and have you signed up to mulesuk yet?
http://mulesuk.freeforums.org/index.php