Without involving paint or expensive new tack all I can think of is ribbons and coordinating clothes. Doesn't have to be solid red white and blue but could be stars or red/white stripes or any combo. Walmart probably has cheap rolls of patriotic ribbon. You could even temporarily cover your browband with ribbon or fabric, maybe even some matching ribbon reins if you feel safe on your horse with them. Of course your clothes should match the colors.
If not that then rig up some colonial soldiers costumes, brown knee pants, blousey white shirt, vest, toy muskets. Horse would probably go natural but you might find some old leather bags at a Second hand store and make some saddlebags out of em. You could google 1776 patriot soldiers and see what they were outfitted with.
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