Can a horse be allergic to carrots or apples?
Horses can be allergic to lots of things. I suspect that the sign is more to deter people from feeding the horse willynilly. One of my horses has heaves and can’t eat dusty things without having a flare. Some horses have laminitis or are prone to colic and even the slightest bit unfamiliar food can cause pain/ injury/ death. Some horses are on very specific diets for the job that they do. Like someone else said, hand feeding encourages begging and mouthiness and eventually biting, so that could also be why they don’t want people feeding them. Regardless the sign is there for a reason, so don’t ever feed a horse that isn’t yours.