While parades used to be fun years ago to ride horses in? I think much of the common sense that people on the sidelines used to exhibit has gone by the wayside.
My friends, who have ridden for many, many years, and drive too, moved here to MO, and the first thing did upon arrival in the small town, was find the saddle club. Joined it just in time for town parade. She said they are riding along, 5 abreast, and the fool on far right? Throws hard candy over all of the horses and riders to his left, hitting a couple of riders/horses, and causing some problems.
She also said that she was amazed at the numbers of children that ran right out into the horses to get a piece of less than a cent candy. Or in front of them screaming.
Most groups in Mardi Gras in Deep South have quit riding their horses in parades because of fools shooting off firecrackers under the horses, or in one case, grabbing the bridles of horses going by and yanking on them. And those parades have MAJOR barricades erected to with law every 20 feet or so.
And last year or so? There was a parade that horse took off through the crowd and killed someone if I am remembering right. Horses stampede at parade kills 1, hurts 20-plus - CNN
Here is the buggy with horses in video shot by bystander.
And this was in Dallas this year, with horse under saddle. Two Injured by Horse at MLK Parade in Dallas | NBC 5 Dallas-Fort Worth
While your skills and the attitude of your horse has much to do with your safety, you can not control what the others around you do, either other riders or bystanders.
Something I always consider? Whether the event would be as much fun, if at the end I have to pay out vet bills because my horse was injured.
Outwalkers are a must, to try and keep people out from under your horses, but even they may do no good.
For me? I would not even think about it, as I value my horses too much to risk injury to them, or to me for that matter.