Dusty Rawhide Saddle

The Zoologist sells this, but not on day one. Saddles enter her stock once your Bestiary is around a third filled, so the gate is exploration rather than gold, and it usually opens on its own during normal play. The three saddles summon the same horse in different colors, so buy whichever you like looking at.

The horse trades everything for flat-out ground speed and needs a run-up to reach it. Short hops between platforms never approach what it can do, so it rewards infrastructure: one long uninterrupted road, ideally a platform highway across the world. Given that, it is the fastest way to cross a map before wings arrive. Halved fall damage is a quiet extra that matters once you are moving that fast over broken ground.

Past a certain pace the horse damages whatever it runs into, so an established road doubles as a cheap way to clear surface trash on a Blood Moon. One flier or one knockback drops you below the speed it needs, so it is not a plan to rely on, but on a clear track it saves you stopping to swing. It will also flatten critters you meant to catch.