In order to examine the striking similarities between the headwear of the background figures and that of Koguryo, we must begin with the Portrait of Friederike Maria Beer—this is our terra firma for obvious reasons, and here the background figures are the largest. The greatest difficulty in proving that these figures are Korean, rather than Chinese or Japanese, stems from the three East Asian countries’ similar characteristics that often only experts can readily discern. The most significant clue is found in the headgear of the figures, which prove that they are dressed in Koguryo style and not Chinese or Japanese style. (For the latter, the figures bear significantly reduced resemblance and probably merit no contention).
In this painting, the figure riding on the brown horse to the far right wears what the archaeologist Sun-Hee Park describes as clearly unique to Koguryo, absent from both the Chinese and the Northern tribes—the two layered hat called cholpung, often decorated with bird feathers. 
A uniquely Koguryo headwear, the cholpung is a cowl-shaped hat with an outer layer around it (shown as a different-colored band). The nomadic tribes wore a vaguely similar hat but theirs covered the neck and shoulders and neither they nor the Chinese wore bird plumage (Park 223). The headpiece of the rider bears an unquestionable resemblance to the Gi Ma Do and countless other depictions of men wearing cholpung in the Koguryo murals, from the paired long, slender feathers to the round button-like adornment directly above the forehead.
According to Park and based on ancient Korean and Chinese manuscripts, the royalty and the nobility wore cholpung made of gold and silver, decorated with feathers or “deer’s ears” made with gold or silver (Park 259-60). The possibility of deer’s ears would explain why they are shorter and more spade-shaped than the more obvious feathers of the rider to the right. Diadem ornaments of the neighboring Korean kingdom of Paekche provide clues to what these “deer’s ears” that were attached to the cholpung might have resembled. 
Paekche diadem ornaments
Another possibility is the gold leaf crown, similar to the one excavated near Pyongyang.
One might doubt the likelihood of this being a depiction of the gold crown, because gold is associated with the king or at least the queen; our figures are clearly neither. But because the Pyongyang crown is gold leaf over bronze, rather than solid gold, we can safely assume that the king’s relatives or higher nobility wore these rather than the king himself (267). Therefore, both the golden cholpung with the “dear’s ears” and the gold crown may have been depicted on the vase; either way, the connection to the Koguryo headdress seems clear.