I was interested in the same question for the Baron's Wars - what did the bog-standard feudal foot slogger have on his shield?
I suspect the answer is - no-one knows.
Later periods, 14th C onwards, show livery colours (usually entirely different from the arms borne by the relevant Lord) and badges. The Feudal period might have had the same arrangement but I don't recall any evidence for it.
The shield might have borne the Armorial colours of the relevant Lord, but the the heraldry is relatively simple at this point and there's a danger of effectively duplicating the heraldic arms - the point of which was to stand out?
Town colours might be possible, in the same manner as football shirts
, again that's true for the later period.
Anything goes might also be an option, but as you note, perhaps unlikely in a more rigorously structured social option. But I quite like the idea of shields painted as gaily as canal boats!
More prosaically the covering might just be plain leather or cloth.
I'd certainly be interested if anyone can point to some evidence for such shield designs, but in the absence of such I'm going to go with a mixture of all of the above, with a bias to the Armorial colours.