As you have not placed any time 'boundaries' on your request, I guess we have to cover the whole period. The following information is summarized from Zhmodikov, Alexander, and Zhmodikov, Yurii.
Tactics of the Russian Army of the Napoleonic Wars, Vols. I-II; Nafziger, 2003.
1796: Dragoon regiments were organised in 10 companies, 2 companies in each of 5 squadrons, each dragoon squadron consisting of 7 officers, 2 trumpeters, fourteen NCOs, and 186 dragoons (theoretical establishment total of 209). Some dragoon regiments were made up of 10 squadrons (rather than 5) at this time. When dismounted, 3 men from each rank in a squadron were detailed to hold the horses, so 6 men per squadron were horse-holders. (Squadrons were always formed in 2 ranks, never 3.)
1802: Formally regiments were composed of 5 squadrons: one general, forty officers, 70 NCOs, 17 trumpeters, and 700 dragoons (828 total). From 1803, each heavy cavalry regiment was to have one half-squadron as a ‘reserve’ squadron, in addition. No details on ‘dismounted’ provided, so I would assume the same situation as per the 1796 regulations.
1810: New regulations from Alexander I abolished the ‘reserve’ half-squadrons, and instead incorporated them into the 5 squadron model of 1 ‘reserve squadron’ and 4 field squadrons on active service. Total manpower was 44 Officers, including 1 x general in each Dragoon regiment, along with 15 NCOs, 3 trumpeters, and 148 privates per squadron. (Thus in the field, in 4 squadrons, an authorised total of 708.) No specific details of horse-holders are mentioned, as dismounted combat increasingly fell into disfavour, and most skirmishing was performed while ‘mounted’.
1812: At the end of the 1812 campaign, dragoons—like all Russian cavalry--were reorganized to the 6 field squadron model, plus 1 reserve squadron (7 total squadrons). Each regiment was therefore now to comprise: 55 officers, 22 trumpeters, 126 NCOs, 1,260 privates (oddly enough equivalent to 209 per squadron, much like 1796). The reality of the 1813-14 campaigns however, meant that regiments typically comprised only 4 or even 3 squadrons whilst in the field.
So, not much detail specific to your request, but it's what I have to hand.
