It's not that hilarious: Poorly equipped troops that survive battles did in fact accumulate better gear.
Considering both rarity of armor as well as some armors like plate needing to be custom fit, you probably would not exceed the most common of, I'd say, chainmail at best, and any sort of common weapons or shields this way.
On the other hand, professional troops are for the most part wearing what they do for a reason, for example mercenary or faction archers would more likely stay in leather.
Ideally it would of course depend on what faction you were fighting at the time. Peasants that help you win against Nords might upgrade into a mix of leather and chainmail, axes and clubs. Winning against Khergits, a mix of leather and scale, bows and spears/lances... etc.
But yeah, units of fullplate mounted knights didn't get that way from looting battlefields.