All orders of battle merely give a snapshot of the army at one point in time: and the Russian Civil War even more so than most wars. What lists we have tend to be associated with a reorganisation, so are much better evidence for the months following than for the months preceding them.
Note: different armies counted differently. The Whites tended to count only actual riflemen as "bayonets" and just line cavalry as "sabres", so not including any supporting troops like machine-gunners. The Reds tended to count everyone in a rifle unit as a "bayonet", whether they served a weapon or not. It is therefore inappropriate to just compare the straight figures directly.
The AFSR was divided into some major groupings. Here are those front-line portions to the east (that is excluding the Ukraine, where the Volunteer Army portion was) at the time of the rejig in Autumn 1919. This side of the army is largely Cossack.
The AFSR was pretty much at its peak at this time:
And this is the force at the Battle of Orel (the Orel-Kromy Operation, in Soviet terminology). It contained many of the best forces of the Volunteer Army.
With the collapse of the drive on Moscow, the AFSR fell back. Some made it to the Crimea, some fled west (the "Bredov March" took many to Poland), but the bulk retired back on the Kuban. This is the Soviet estimate of the forces there.
After the loss of the Kuban, the AFSR became the "Russian Army" under the leadership of Baron Wrangel. There were a great many rearrangements, both big and small, and units in the orders of battle might have no equipment or be made up more or less entirely of POWs. Orbats for this period must therefore be used with great caution, as they were out of date even as they were being made.
The Trans-Dnepr Operation by Tom Hillman has good orbats in the back relating to the forces involved.
The design notes for the board game Tachanka! have a useful list of the units as they evolved in the south.
This is the White Russian units operating on the Estonian border up to May 1919.
(Maps showing the positions of the above units of the Northern Corps in May, and the extent of their offensive can be found in the maps section.)
By late 1919 the Whites in this area were called the North-Western Army, and under the command of General Iudenich. Although not actually doing much fighting, their reluctant Estonian allies propped up the southern wing. This is the list of units pretty much at the peak of the second drive on Petrograd.
The short-lived KOMUCH was never a great power but its campaigning in co-ordination with the Czech Legion was the first serious threat to Soviet power. Information about the People's Army is hard to find, hated as it was by adherents of the extremist elements that came to dominate the early writing up of the war, both Red and White.
Kolchak's units underwent a kaleidoscopic change of organisation as the fronts swayed back and forth huge distances. Just before his peak we have a fairly full list. Because it is so long, it is broken into sections.
The arrangement of the army in the period just before, and their opponents, can be seen in this map.
The Urals Cossack Host was formally part of the main White forces in Siberia, but operationally it kept separate. The Ataman commanded non-Cossack forces and parts of other Hosts, and various orders of battle deal with those in different ways. The Urals Host appears to have had both territorial and numerical naming systems, which makes tracing units difficult:
The Orenburg Cossack Host is very difficult to keep track of. Ataman Dutov commanded large numbers of non-Cossack forces, but at the same time many Orenburg Cossack regiments were dispersed to other commands. These orders of battle do not list all the Orenburg units, just those in the main Orenburg theatre.
Independent Semirechensk Army mid 1919 (and opposing Red Forces)