I noticed newly installed fence board have wet bottoms after raining. I
think water is wicking up from the bottom of the fence board.

Would painting just the bottom (the side that faces the ground) of the fence
board (a 4x1 cedar) fix this and prolong the life of the fence? Since it's
impossible to repaint the bottom once the fence is installed, whatever
paint/stain/sealant is used should last 10 years or more in an outdoor
environment. Any suggestions?