Parkhaev's drawings of the 1812 army show the trumpeters mounted on white/grey coloured horses and a kettle drummer mounted on a black horse.
STAFF TRUMPETER OF THE YEKATERINOSLAV AND TRUMPETER OF THE ORDER CUIRASSIER REGIMENTS
STAFF TRUMPETER OF THE MOSCOW DRAGOON REGIMENT
STAFF TRUMPETER OF THE MARIUPOL HUSSAR REGIMENT
TRUMPETER OF THE LITHUANIAN LANCER REGIMENT
KETTLEDRUM PLAYER OF THE CAVALRY GUARDS REGIMENT
The copy in my possession shows a much darker horse – hence my comment about black.
Only information I could find in Viskovatov (from Mark Conrad's translations):
30 April 1802
Cuirassier horse— no taller than 5 feet 3 inches, and not shorter than 5 feet. There is no prescribed colour, but the cost, less delivery fee, is authorized to be 100 roubles.
16 December 1815— In Cuirassier regiments, trumpeters are to have grey horses, and other ranks — dark colours.
30 April 1802
Dragoon horse— no taller than 5 feet, and not shorter than 4 feet 10 inches. There are no prescribed colours, but the cost, less delivery fee, is authorized to be 50 roubles.
16 December 1815— In Dragoon regiments, trumpeters are to have grey horses, and other ranks — dark colours.
30 April 1802
Hussar horse— no higher than 5 feet tall, and no less than 4 feet 8 inches, of no particular prescribed colours, but authorized to cost 40 roubles not including delivery.
Guard Cuirassiers
16 December 1815 – It was directed that trumpeters in these regiments have gray horses, and other ranks—dark colours.
Guard dragoons
16 December 1815 – Trumpeters were ordered to have grey horses, and other ranks — dark colours.
Guards Horse-Jäger Regiment
13 March 1816 – When assigning remounts to the L.-Gds. Horse-Jäger Regiment, it was ordered that any colour horse be selected except light bays [solovye], Isabellas [izabely, i.e. palominos], spotted [chubarye], sorrel or light-brown Tatar breeds [kaurye], light chestnuts tending to yellow [savrasye], and pigeon grays or ash colors [golubye].
Guard Hussars
13 March 1816 – When assigning remounts to the L.-Gds. Hussar Regiment, it was ordered that any colour horse be selected except light bay, Isabellas [i.e. palominos], spotted, sorrel or light-brown Tatar breeds, light chestnuts tending to yellow, and pigeon grays or ash colours.
Guard Lancers
16 December 1816 – Trumpeters were ordered to have gray horses, and other ranks to have dark colours.
13 March 1816 – When assigning remounts to the L.-Gds. Lancer Regiment, it was ordered that any colour horse be selected except light bays, Isabellas, spotted, sorrel or light-brown Tatar breeds, light chestnuts tending to yellow, and pigeon grays or ash colours.
