Will McLean has a good entry on the use of various heraldic signs in time of war. Here's the most interesting bit:
When did men-at-arms wear coat armor, and when did they wear something else? It's a complicated question. [The ] closely related Agincourt accounts of Jean Le Fèvre and Jean de Waurin shed light on who wore coat armor and when.To tell the truth, the king of England had wanted to lodge in another village which had been taken by his herbergers, but he, who always observed proper and honourable practices, did what you will now hear. It is true that whenever he wanted to send scouts before towns or castles or any matter, he had the lords or gentlemen take off their coats of arms when they went off and put back on again when they returned. It it so happened that on the day that the king left Bonnières to go up close to Blangy, there was a village which had been commandeered by his harbingers, but he had not been told of it. Not knowing in which village he was supposed to lodge, he went on by a bow shot and rode past it. Then he was told he had passed it. Then he stopped and said 'As I have passed, god forbid that I should return as I have got my coat of arms on'. And he moved on and lodged where his vanguard was lodging, and moved the vanguard further forward.
...But to return to the king of England, before he crossed the river at Blangy en Ternoise, because the crossing was narrow he had six bold men of his vanguard take off their coats of arms and cross over in order to find out whether the passage was guarded. They found that there was no one seeing to its defence, so they crossed quickly.
From these accounts it appears that coat armor was particularly associated with pitched battles, and that anything that could be considered retreat could be considered dishonorable once it was put on. For that reason Henry did not want it worn when scouting, because the men would necessarily have to return to the main body, and this could be described as retreat. Also, coat armor was worn not only by commanders, but by at least some of the ordinary gentlemen.
Later, Le Fèvre and de Waurin tell how Anthony, duke of Brabant, rode in such haste to the battlefield that he left the main body of his men behind.
As he would not wait for him, because of the haste with which he had come he took one of the banners from his trumpeters, made a hole in the middle of it, and used it as his coat armour.
So, the duke did not have coat armor with him on the march, but thought it so important to wear it in battle that he made improvised coat armor from a banner.