How can I open my horse's inventory?
According to the player manual you can bring up the companion command menu by long-pressing E while aiming your reticule at a companion. I would assume the same philosophy holds for horses, but I am unable to make it work.
Is there any other way to bring up my horses inventory? Or am I simply misinformed?
Only human companions have an inventory, your horse does not. However, your horse will allow you to carry more than your normal load and travel at full speed.