Does placing electrical cables in a fence between two structures meet electrical code?
Given that the horizontal studs are 1.5 inches deep plus the depth of the vertical planks being .5 inch ( guessing ) total depth is 2".  This is a good thing but, and I am going to have to emphasize the but, ..... this is not normal and given the amount and size of wires in there I am not comfortable saying this is okay.  But what do I know, I'm only a licensed master electrician who runs his own insured company. ;-)