Age of Conan, you are probably extremely unimpressed with your new companion's speed -- it almost seems like you don't move any faster at all. According to this post at AoC's official forums, this is in fact the case. One of the game's designers has confirmed that, currently, even the mighty horse trots along at regular run-speed. A proper fix for this is coming in a future patch, but a temporary workaround is shared for now (which a lot of people in the community had already figured out): simply sheathe or unsheathe your weapon while mounted, and enjoy the mount's speed boost as it was intended.
Also included in the post is the fact that the speed boost itself will be increased very soon. Horses will be slightly faster, and Mammoths and Rhinos will get a smaller boost. As well as this, to address a complaint that those with Mammoth/Rhino pre-order privileges have, the riding skills (charging, attacks, etc.) associated with these mounts will be given automatically with the "/claim" command after a future patch, and those who already have the skills through buying Basic Riding will need to perform the command to receive them again.
EDIT: Going by this forum thread, the mount speed increase is already in effect as of today's patch. Some in-game testing of our own shows that at the very least, the bug requiring weapon sheathing/unsheathing is fixed. More on these other undocumented patch changes shortly.