When I married I moved from CA to a state 2000 miles East. My new husband and I hauled my 2 horses in my straight load BP trailer. We did stop overnight at various " horse motels" ( it was 27 years ago) and we took 5 days.
My horses did just fine.
Hauling from Iowa to Mississippi is certainly doable. We have hauled up to 16 hours with just stopping for gas and a quick meal when we moved multiple times over the years. I now have a 16 foot stock trailer so they have much more room.
I would always choose hauling my own over a commercial shipper.