There are mods for that if you're on PC. Every game since Morrowind has had mods to allow backpacks and multiple containers. It can actually be really helpful to have an ingredient bag, for example, either in your backpack or in your inventory. But yeah, I've often thought saddlebags and a packhorse would make a lot of sense.
Morrowind actually had http://www.uesp.net/wiki/Morrowind:Pack_Guar in the game, but IIRC you could only really use them with mods.
There's also something that you can 'acquire' in Solstheim if you have Dragonborn, though it's probably 2/3 of the way through the quest.
Spoiler
http://www.uesp.net/wiki/Dragonborn:Dremora_Butler, but max carry weight is only 148.