Saint Barbara is celebrated as the patron saint of the Artillery Corps of the Greek Army and the Cypriot National Guard. Artillery camps throughout the two countries host celebrations in honor of the Saint on December 4th, where the traditional sweet of loukoumades is offered to soldiers and visitors. This tradition began in 1829, allegedly because the loukoumades resemble cannonballs.
However, according to the Hellenic Army General Staff website, the reason the Artillary Corps has Saint Barbara as its patron saint is because lightning struck and killed her father after he beheaded her, and this punishing lightning symbolizes the fire of the artillary. And on 4 December 1829, when this patronage was established, the event was celebrated in the camp of the first "Battalion Order", as they were then called, with traditional loukoumades and cognac.The tradition stuck ever since.
It should also be noted that since this feast lands during the Nativity Fast, and dairy products are forbidden, loukoumades with honey, cinnamon and nuts is an obvious alternative for a festive sweet. This may be why in Greek villages, where they have a church dedicated to Saint Barbara, they serve loukoumades to celebrate, and this could predate 1829.
