Buildings on the same lot as a single family dwelling are considered as accessory to the dwelling and the same building code rules apply to those buildings.
But, all wiring must be done using wiring methods appropriate for the conditions of use.
Also, if the wiring in any location is subject to abuse of any kind, then you must choose a wiring method that can withstand such abuse or provide protection for the wiring method used.
A horse barn on a residential lot is subject to the rules of Article 547, but COULD be wired with NM in clean, dry, protected areas. There are no habitable areas in a horse barn, and power is not even required to accessory buildings.
Looking at the scope of Article 547, I see that only those agricultural buildings or portions of those agricultural buildings that have excessive dust, water or corrosive conditions need comply with the requirements of 547. (Note also 547.3)
So, all things considered, NMC is OK. If you are concerned about possible rodent abuse to the wiring, then protect it: run rigid, intermediate, EMT or PVC conduit