There are two properties of a material that matter related to ESD (ElectroStatic Discharge): How much they generate static electricity when they rub against something, and how well they bleed off any charge that might accumulate.
Being even a little bit conductive helps a lot in reducing ESD problems. It's hard to generate lots of static charge, so a little bleeding off of the charge usually keeps it below the level where it can cause damage. Unfortunately, nylon is a very good insulator so won't help much in bleeding off any charge.
I don't know the properties of horse hair in this regard, but it's quite possible that it has lower bulk resistivity, especially when there is some humidity in the air. Perhaps horse hair produces less charge when rubbed. Materials vary in that regard, and I don't know about horse hair. Cat hair is notorious for generating charge, especially against rubber. Human hair is fairly good when clean. Think of rubbing a balloon against your hair. You can usually make it stick to something after that due to its static charge. Dirty hair or hair with various conditioners in it (really a form of deliberate dirt) works less well because the dirt provides a bleed path for the static charge. Some conditioners do this deliberately. Perhaps horse hair has this sort of thing built in. You'd have to ask a horse for details, or failing that perhaps your professor.
In any case, he's probably right about nylon being a bad idea.