Much of controversy regarding the early Mongol weaponry to the West of Urals is due to the fact that it is separately researched by those specializing in texts (Kuleshov?), miniatures (Gorelik) and archaeological finds (myself).
The case of miniatures is especially interesting and important. They do present Mongols as exceptionally well armored force, with an emphasis on swordfighting. They also, at least the earliest, 14th century examples, do show evidence of some East Asian influence (helmets with protruding “ribs” which would normally identify lamellar plates, from which almost all East Asian helmets are assembled).
Indeed, very roughly 70% of encounters are swordfights, 20% are done by spears, 10% is everything else combined. Participants are either obviously armored, or well dressed in a way which might conceal some armor underneath.
So why in my opinion this is not the evidence of Mongols per se being superior and self-sufficient in sword and weapons production and usage?
First, the earliest (13th-14th century) miniatures tend to show identically armed warriors. This is obviously a convention – one miniature shows everybody with swords, another – everybody with spears etc. This does not bode well for the whole question of using them to determine percentage of warriors armed in a specific way – one artist in one cycle would arm everybody with swords, another one – with spears, and whether percentage of artists drawing swords correlates with their usage on the battlefield is hard to ascertain. For example, miniatures very seldom show someone killed or shot at with a bow, which is inconsistent vis-a-vis the period texts. It was obviously considered a less honorable fighting compared to hand to hand sword combat, and probably for this reason alone, it is seldom addressed in miniatures, to the point that most warriors don’t even have bowcases!. Not surprisingly, WWII paintings also disproportionally show close range or even hand to hand combat, with pathos, heroic postures and other elements of militaristic beauty, but often little relation to the historical events.
Second, even if we to accept that the number of artists/works depicting swords does correlate to the percentage of troops armed with swords, there is no certain evidence that the troops depicted are all Mongols and not their numerous vassals, many of whom indeed were less inclined to use bows as a primary weapon. Even in miniatures there is some supporting evidence of such regional variations, for example, period Georgian miniatures on average more often show people armed with spears.
Third, and main point, is that the earliest miniatures show swords that are consistent with the period Pontic-Caspian examples (with asymmetric guards), maybe even more so even than with earlier Seljuk swords (decorated blades, more simple guards), and certainly nothing alike the East Asian examples, with tsuba guards etc. The ribbed helmets shown certainly otherwise are quite similar to the earlier Caucasian tall helmets. The “ribs” might be decorative, as we do see on some existing 16th century artifacts. Not many 14th century helmets survived, but all of them are also clearly consistent with pre-Mongol examples, rather than East Asian, riveted, models.
In short, there is nothing in miniatures that clearly points towards any substantial influx of the East Asian tradition. While the Mongol armies do appear heavily armed and armored, which might or might not be a stylistic exaggeration, there is definite continuity vis-a-vis the preceding Cuman (Kipchaq) period.