It's not that Fae are allergic to iron, cold or otherwise... except in modern faerie stories. Fae are the antithesis of technology, and so are in opposition to what was the height of technology of the day, ie, iron and steel. Fae are also in opposition to civilization in general, including orchards, plowing (particularly plowing), buildings that aren't tents, money, and so on and so forth.
Fae are chaos embodied. They represent everything medieval peasantry feared-- that being nobility, the weather, the wilderness, wildlife, disease, crop failure, etc. They have power without reason. And just about anything that you might do to try to survive in a messed up world will piss them off, and you don't want to piss them off, so you do whatever you can to placate them, otherwise WORSE THINGS WILL HAPPEN.
Faerie stories are horror stories.
But anyway, while civilization pisses them off, it can also drive them back if you have enough of it. The trouble is, out on the farm, you CAN'T have enough of it. But then we get mixed up in some voodoo and hedge wizardry. Just like you ward off enemies of the church off with symbols of the church, ie, the cross, you can sometimes ward off enemies of civilization with the symbols of civilization. IE, "Cold Iron" (as in the phrase, "Have a taste of my cold steel, you mfing bastards!"). Worked metal. Originally intended to mean swords and axes and such. The stuff that keeps the forest at bay.
This then gets mixed in with MORE superstition about gates and traps and things, so it turns out that the best thing is to have iron with holes in it (it's complicated and almost nonsensical). So what you really want is an iron horseshoe, as a perfect representation of civilization, in iron form, with holes in it.
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You can't tell I've written term papers on the subject, can you?