Agreed a bag is need and maybe a mount bag too. Mount can be packmule.
Maybe the bag can also add saddle to the horse model. From simple saddle to heavy cavalry armor.
Interesting idea. If it was me, I would make it that someone can still loot it if you leave your horse out, but as long as you are mounted they can't touch it. Some extra inventory, but still requires you to work for it to get it and to use it. Yes, I like this idea a lto!