I don't know about Medieval Europe, but there was a push toward uniformity in Medieval Japan. I'm counting Medieval Japan as the Sengoku period (1470-1570), just to clarify. That hundred year period is when the Japanese developed formation fighting, mostly fighting with spears. Families starting creating some uniformity among their soldiers; they'd pay for armor, helmets, and weapons for levies and "samurai" would receive a sort of small flag that marked them as being part of a particular army.

While armor might not be painted "family colors", helmets and sometimes chest pieces would have the family crest painted on. At a bare minimum, battle standards would bear some sort of defining crest.

Heraldry was never really used as a means of identification on the battle field to begin with according to Cannan Fergus. Because in the heath of a battle it was impossible to recognize every individual coat of arms. The coat of arms were used asside from the battle field as a status symbol. On the battlefield they were usefull because they could be used as a sort of predecessor of the army tag. Furthermore was it common that noblemen changed their coat of arms in their lifetimes (Charles VI in the hundred years war for example). Heraldry was also not exclusive to noblemen, Guilds used, and the church also used its fair share in coat of arms. In conclusion no there was no real uniformity in armies, although that could differ from region to region. Noblemen used their coat of arms more as status symbol. There was however livery clothing, but that wasn't really used on the battlefield.

Source

F. Cannan,“The myths of medieval heraldry”, in: Nothingham Medieval Studies, 47 (2003), 1.

In England in the Wars of the roses, men at arms and archers retained by a lord would wear his livery colors and badge. This could be distinct from the colors and devices of their lord's heraldry.