The two Vegetii

[Nathan Ross]

Did a bit of digging here are the Theodosian Code titles you mention.

Good digging - thanks!

(comes sacri stabuli), a minor count whose chief function was to provide a supply of horses for the military.

Although there doesn't appear to be anything in the two passages from the CTh that connects this role directly with horse supply. Instead, equine business seems to be entirely in the hands of the Stratores.

And the guiltless man would have suffered a cruel fate, had not Cerealis, the tribune in charge of the stable, at the risk of his own life postponed the terrible wrong. 

So here we have a tribunus stabuli at least in a stable and in proximity to a horse!... But nothing here, I think, connects Cerealis with supplying horses to the army though.