Okay - having done some research on the 23d:
[This] is a shot of the mannequin that was donated by the recreated regiment to the Regimental Museum in Caernarfon Castle, Wales. By the way - the cap plate on that cap was donated by ME. I wore it for many years in that group before becoming a Guardsman.
AUGUST 15, 1780 (War Office Dorchester (Carleton) Papers, PRO 30.55:25 No. 2967)
Sir. (Gen. Clinton)
I have the honour to send you the enclosed List of Regiments belonging to the Army under your Command for which Clothing for the present year has been shipped on board the Prince George Transport. . . . (signed)
Return of Clothing etc, shipped on board the Prince George Transport for His Majesty's British Forces in North America, Commanded by Sir Henry Clinton and compleated 10th August 1780.
N.B. Hats only are sent for the 23d Reg't, the Commanding Officer having reported to their Agent from North America sufficient of other Articles in Store. . .
So, they were wearing HATS, not the Fusilier caps, at least some of the time. What those hats looked like is subject to conjecture. Don Troiani did the painting of Cowpens showing the 7th Foot, Royal Fusiliers, in cocked hats and brown trousers if memory serves. That was based on some information from Jim Kochan and other sources. All three Fusilier regiments used the same regimental agents and what one did, the others seemed to do. There's no question that a lot of units had brown trousers in the Southern campaign. The Guards did and the 33d did as well as others.