I simply assumed horses (and Tanar'ri) simply died out sometime between 3rd and 5th edition D&D. Point 3 is possible already, however: My camp was illuminated by purple Illithid tanks, had a necromancer lab with bones and all the useless glassware you can find everywhere and usually held a smattering of current quest items, books and other stuff, liked brain jars and the Resonance Stone. You can grab many things and send them to your camp, if you don't want to carry them around. You don't seem to have your own tent if you're playing as Tav though.