Not seen any refference for mounted drummers (bar kettle drummers) past the ECW period Dragoons. They could well have gone in to the restoration period having said that, but there's a big gap between Dragoons fighting dismounted (for the 2nd it was 1707 up till WWI), although I think some fought dismounted during the 1719 rebelion.
Anywho - Crimean period - not a chance. Dragoon by name, cavalry by nature. Field service musicians would be relegated to Trumpeter.
The best one I know on that score is Neil Wishart who knows just about every call for both dismounted (parade, mounting up etc) and mounted (change of pace, turns, drawing swords, putting up sword, charge and more importantly recall.
In fact here he is in the Crimea for the 150th
(just don't look at the dressings - I missed this as I was in Helsinki, but apparently the horses were interesting
Young men have often been ruined through owning horses, or through backing them, but never through riding them: unless of course they break their necks, which, taken at a gallop, is a very good death to die