I have NEVER heard anyone recommend feeding horses eggs... EVER. We are the only mammals on Earth that continue to drink milk products past "weaning" time, so that argument doesn't cut it.
Horses are herbivores. The only type of animal it's "fine" to feed eggs is one that is an homnivore, or a carnivore. Herbivores eat plant matter, plain and simple. Biology 101.
There are plenty of crazy old-timer stories and "recommendations" out there. So I'm not too surprised to hear such non-sense. Tabacco used to be fed in large amounts to get rid of internal parasites. Other old wives tales include women not working around studs during menstration (total BS), white hooves aren't as strong as dark hooves, witholding water to a hot horse, chestnut mares are ill tempered, etc.
There are a few highly concentrated ration balancing feeds out there that use "egg product" in their formulas, but they use a process to exctract only the targeted amino acids from the eggs and put that in the feed. I still think it's hinky, but it's nothing close to feeding a horse any part of a raw egg...