I have always associated the horseshoe with the 37th Division but a reading of Ray Westlake's excellent Kitchener's Army has put me right.
"25th Divisional Sign. The 25th Division had two signs-a red horseshoe was worn on the uniforms, while an oblong of red and white check was painted on vehicles and signboards".
I think that having TWO divisional signs is cheating.
Simon