Schedule 40 and 80 PVC would be IMO, the way to go in a horse barn. (80 where exposed).
You want to keep the wiring as up high and protected as possible. Also you might consider putting a switch in a remote location to turn the barn lights on. Also use lighting that will come on instantly without a warm up period.
Horses can get into lots of trouble, and it's no fun trying to go into a dark barn to try to save them.
If the lighting is suspended from ie: chain, and connected with a short section of LTNMFC, vibration and shock won't be transmitted to the lamps, and they will last longer.
I used to care for 100-200 horses (in Riverside County, CA
) My boots would usually last < 3 months, even with constant care. Now I get a year or so out of them.
Armored Cable without a jacket, like iwire says, would not last much longer than my old boots. It's really that corrosive of an environment.