These two skulls, alongside others from Montana's Bear Creek, were reported on briefly by Sigogneau-Russell and Donald in 1978, who regarded them as evidence for the presence of the Eurasian genus Simoedosaurus in North America.

Additionally, all of the skulls show that the cranium of Kosmodraco was exceptionally flat and covered by ridges and furrows along the dorsal and lateral surface.

The external nares make up around half the width of the bulbous premaxilla and are partly divided by the fused nasal bone.

[3] The paired prefrontals are anteriorly bifurcated by the nasal and reach to almost the exact halfway point between the orbits where they meet the rectangular frontal bones.

Almost the entire medial border of the supratemporal fenestrae consists of the parietal bones, which display a long suture along the center of the skull.

The infratemporal and supratemporal fenestrae are similar in size and the maximum distance between the squamosals is only slightly larger than the width of the skull table.

The first three alveoli of the premaxilla are twice as large as any following (except for two where the maxilla is relatively inflated), which differs from the more consistent decrease in size observed in the teeth of the type species.

At around the end of the anterior third of the maxilla, the bone is ventrally inflated by two enlarged maxillary alveoli in a condition comparable to the area right behind the premaxillary-maxillary suture in the type species, however greatly exaggerated in a manner more akin to modern crocodylians.

However, unlike in the holotype, these nodules are much more developed, exceeding any other late Mesozoic or Cenozoic choristodere and much more resembles those of Coeruleodraco and Monjurosuchus.

Among the cervicals, the axis has a stout neural arch and large crest that projected over the centrum of the atlas, likely as an anchor for the musculature of the head.

K. magnicornis was on the smaller side of the spectrum with a skull length of 431 mm (17.0 in), which still leaves it as the fourth largest known choristodere behind K. dakotensis, Champsosaurus gigas and Simoedosaurus.

[3] Phylogenetic analysis consistently recovered Kosmodraco as clading together with the Old World choristodere Simoedosaurus and Tchoiria, forming the family Simoedosauridae within Neochoristodera.

Within the phylogenetic analysis conducted by Brownstein, differences within Simoedosauridae are restricted to the relationships between the two basalmost taxa, both species of Tchoiria.

[1] Kosmodraco additionally shows that both the orbits and nares were raised, an adaption to a semi-aquatic lifestyle commonly seen in crocodilians and absent in gars.

These attachments for sacral and caudal soft tissue differ from what is observed in crocodilians today and make it subsequently difficult to infer the precise ecological niche these animals would have inhabited.