How soon would 4/4-by-6-by-8 white oak boards be ready to use as a horse fence? I have been told that right off the mill is O.K. Is it more prone to warping?
Because these boards will be largely unrestrained as they dry (compared to being in a stickered pile of lumber), they will be freer to move as they respond to stresses. Because the air circulation around them will be tremendous, they will dry very quickly, at least on the outside. And since this is oak, they will likely surface check heavily at the rays.
Is this a problem? I dunno, it depends on you. The warping is relative. They're not going to jump off the fence (at least most won't), but they will probably warp more than they would if they were dried in a stack first. On the other hand, if they're low-grade oak, which I would presume they are, some of them will move around pretty substantially even if they're in a stack.
On the third hand (if I had one), whatever warping you will get will probably only be noticeable by passersby when they're in a position to look straight down the fence, when every deviation from linear is visible.
Consider weather and how you intend to finish the fence. If you will be painting it, think about air-drying first. You shouldn't paint green lumber because the moisture in it will cause the paint to peel. If you put it up green and then paint it once it's dry, the surface checks that will open up at the rays from too-rapid drying will be difficult to seal effectively, and when water inevitably works its way in there, again, the paint will fail. If it will be allowed to weather unfinished, this doesn't really matter.
I personally have never built fences out of white oak, but I've built a lot of horse stalls out of green oak, in fact I built a 40-by-44 two-story horse barn out of it. Framing with white oak must be done with green lumber because it's too hard to nail once it dries (darn near too hard green, for that matter). At any rate, green lumber works fine for stalls. I've usually used 2-by-6 or 2-by-8.
The only other issue I'd raise is that green lumber is much more flexible than dried lumber, and if it's put under too much stress while it's green, it will "take a set," meaning it will dry in a deflected (bent) form -- the same principle at work in green-bending chair parts.
If you're using 4/4-by-6 material in only 8-foot lengths and the only load is the board's own weight, then there shouldn't be a problem, provided the boards are installed on edge, as I presume they will be.