I'd paint it with a 30% mixture of linseed oil and turpentine. Mix it good as the turpentine is just to get the linseed oil into the wood, and it sprays easily.....don't have to worry about holidays, or spots where some wood absorbs more paint than others making for a light spot.
Let it mature naturally. Fence will last a lot longer and you won't have moisture problems and a "needing painting" fence a few years down the road....unless you just like to paint pickets.
I do the same thing on pipe. Learned the trick at the DFW airport. Put up the fence and walk away. Before long nature will paint it for you in the most beautiful copper brown (earth tone, blends right in with nature) and keep it painted, nice and uniform every year at no cost. Doesn't hurt the pipe. Iron oxidizes forming a thin skin providing insulation between the steel and the environment.