She wears some sort of skintight garment under her armor -- a spandex leotard? A catsuit?

One of her calling cards is the metallic clangs from her shoes. is calling them shoes right? Not sure if sabaton works, and that's a bit obscure I think. Is there a better term? The princesses wear more ornate finery, but I'm not sure what's the best name for them either.

Metal brace around the front of her neck = peytral?
Shoulder = pauldron?

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"Tempest Shadow... a mare of a ferocious standing and even more ferocious visage, bearing darkened armor that covers her slim, but firm frame, offering immense protection from those who would seek- no, dare to harm her. Upon her hooves are armored shoes that offer not only solid defense and comfort, but amplification for many a devastating attack from their iron edges, which she used many a time to trot over those who would defy her. Beneath the grim armor lies a suit of soft, expandable cloth, pliable and thick, like a loathsome spider's web of shadow meant to aid in holding her metal carapace together and keep her flesh from suffering its discomfort. Upon either shoulder rests a mighty pauldron of masterful making, having saved her body from harm many a time from a roving blade or cast spell. However, no part of her armor or arsenal is nearly as imposing, nor deadly as her sinister cunning, terrifying, and determination, relentless..."

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Look up horse armor on google. There are diagrams.

You could call her leotard a gambeson if you wanted to be really fancy. I mean, that's actually a paded jacket but it WAS worn under armor as padding.

Also everybody knows what Tempest's armor looks like, so you don't really need to describe it unless something's happening to it.

I'd like to imagine it as a special type of new-age breathable Kevlar. And her armor as being made of a lightweight Kevlar and aluminum alloy.

For the way she jumps, leaps, and kicks, you cannot do that with heavy metal on your body - it'll weigh you down.