Spoke with a miniaturist and a dioramist who is also a dealer in antique military goods.
The consensus is that color in the British and the French Imperial service was used to differentiate between regiments not branches of the service.
Considering the plethora of lights, heavies, dragoon guards, hussars and cuirassiers they raised, its not surprising. I seem to remember the French 5th Cuirassers in Germany in the 1980's. Also outdrank some guys from the 9/12th Lancers (Prince of Wales Own) one night.
Even before the reorganization of 1861, when the US had multiple types of mounted troops, there were at most five regiments so we didn't have that problem.
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