Back when World of Warcraft vanilla first launched, the epic mounts were simple recolors of the level 40 versions of the mounts. This meant that they looked almost like them, but ran at 100 % speed. It was pretty difficult to get these mounts back in the day, and when patch 1.4 hit the server, these mounts were removed from the mount vendor and replaced by the epic faction mounts we still have today. All the players with the old epic mounts also had the opportunity to trade it in for a new mount, and a lot of them did. This means that the old unarmored epic mounts became incredibly rare, but will we be able to get them in World of Warcraft: Classic?
Unfortunately the answer is no. It will not be possible to obtain the unarmored epic mounts in World of Warcraft: Classic. Blizzard said this was to prevent people from rushing the vanilla experience, and that they have no plans to ever release them on live or classic servers again.
So if you were hoping to get your hands on one of these mounts, you're out of luck, because it will not be possible. Instead the regular epic mounts will be for sale from the mount vendors.