Many
people attribute the circular barn sign designs to the German
culture, however the barns in Germany are not decorated!
There are, however, many circular geometric designs in various
cultures, and traditional designs are often used in the
painting of hex signs. These traditional designs may or
may not have "magikal" symbolism.
It
is hard to track down the history of the designs in the
US, as there is much dispute over the nature and purpose
of hexen. Many old timers insist that they were painted
"just for pretty" and as old barns fall into disrepair,
or are repainted, the designs are left to weather away or
painted over. Not every farmer wants to have tourists at
the gate, snapping pictures of the "picturesque"
barn! 
Other
folks may admit that "once upon a time" the designs
were attributed with "magical" properties of protection,
or as a talisman of fertility for livestock and crops, or
invocation for a balance of rain and sunshine. But that
was then... OR WAS IT?