Cavalry and chariots against infantry

[Domen]

It's the purpose - to make the emperor seem invincible - that makes it propaganda.

A similar purpose was to make Henry V invincible after Azincourt... That makes propaganda.

Ammianus' account contrasts the Huns, genuine pastoralists, with the Goths.

The Goths were not a monolith - a homogenous, one tribe - various branches had different lifestyles.

Thervingi (their name literally means "people of the forest") were not the same as Greuthungi (their name literally means "people of the steppe"). Gradually they were assimilating with each other, but during times of Adrianople they were much different, as they came from different environments.

Thervingi lived closer to the Roman border (just behind the Danube river). Perhaps Ammianus was thus describing customs and lifestile of Thervingi, as he knew them better than steppe Goths.

How many of them were able to smuggle horses across the Danube?

All of them?

In exactly the same way as they managed to "smuggle" themselves across the Danube.

How many of the refugees were soldiers, as opposed to civilians

What "civilians"? In the Gothic society there was no such thing (only women and children).

But every man between ca. 15 and ca. 50-60 years old in the Gothic society was a warrior.

Of course apart from being warriors many of them also did something else for a living.

there's nothing in it to show that it represents the stand of the Praetorian Guard as opposed to the rout.

It can't be determined for sure whether it represents the stand or the rout.

But it is more than clear that it represents hooves of horses trampling down people.