I have a shed that is wired via grey Schedule 40 PVC that runs underground
from a GFCI receptacle under my deck. The shed is up against a wooden
board-on-board fence similar to this:

http://rtfence.com/wp-content/upload.../12/wood12.jpg

I'd like to add a receptacle on a fence post about 15 from the shed. Can
I
come out of the shed with Schedule 40 conduit and run the conduit either
on
top of or underneath the lower horizontal member of the board-on-board
fence? This would mean that the conduit would be between the vertical
slats
of the fence for the full 15.

If not, is burying the conduit and using a riser stub up my only other
option?

*Yes you can. Be sure to use an expansion coupling. As someone else
mentioned, painting the pipe would make it less noticeable.