The main source of information for this is gorynych forum, a site devoted to the history of the Urals Cossacks.
This order of battle basically represents the Urals army from Spring 1919, when most units were reformed following the difficult Winter. It lasts more or less the same until October 1919, when ad hoc groupings of the remaining steady units started to take over.Another version, (with bayonet/sabre/MG/gun numbers) is available, but appears to have some omissions and errors.
1st Ural Cossack Division
1st Ural Training Regiment
3rd Ural Training Regiment
Guriev Cavalry Regiment
Kalmykov Cavalry Regiment
Guriev Foot Regiment
1st Ural Horse Artillery Divizion (1st and 2nd Mounted Batteries)
2nd Ural Cossack Division
Lbischensk Cavalry Regiment
Uralsk Cavalry Regiment
Sakharnovsk Cavalry Regiment
1st Partisan Cavalry Regiment
2nd Partisan Cavalry Regiment
Composite Foot Regiment
2nd Ural Horse Artillery Divizion (3rd and 4th Mounted Batteries)
1st Urals Infantry Division
This unit seems to have operated as separate regiments.
33rd Nicholaevsk Infantry Regiment
Semenov Infantry Regiment (or Volga Semenov Druzhina)
5th Urals Infantry Regiment (or Tsarevski Regiment)
3rd Ural Cossack Division
This Division was not formally formed until May 1919.
Rubezhensk Cavalry Regiment
Kirsanovsk Cavalry Regiment
Foot Divizion of Captain Domashnev (or Rubezhensk Foot Divizion).
5th Mounted Battery
4th Iletsk Cossack Division
This Division was not formally formed until May 1919. It seems to have been mostly operated over a very wide area.
2nd Ural Training Regiment
8th Cavalry Regiment
16th Cavalry Regiment
Iletsk Foot Regiment
6th Mounted Battery
5th Ural Cossack Division
This Division was formed in June, having previously been the Burenin Brigade, consisting of the Irtetsk and Burenin Regiments and a four-gun battery.
Burenin Cavalry Regiment
Irtetsk Cavalry Regiment
Northern Partisan Cavalry Regiment
7th Horse Battery
6th Ural Cossack Division
This Division was transferred to 1st Corps in about August 1919.
Slamihinsk Cavalry Regiment
Chizhinsk Cavalry Regiment
Korzhevsky Partisan Detachment – 2 squadrons.
1st Training Battery.
The Pozdnaykov Regiment later became the Novouzensk (Non-Cossack) Cavalry Regiment.
1st Astrakhan Cossack Regiment
Volga Partisan Cavalry Regiment
1st Astrakhan Cossack Plastoon Regiment
2nd Krasnoyarsk-Yenotaevsk Cossack Plastoon Regiment
Astrakhan Artillery Divizion
This corps is often omitted from Host lists and numbers, as it was composed entirely of non-Urals units and fought separately from them. It held the front towards Astrakhan along the Caspian.
The Astrakhan Cossack Regiments were from that Host. The other two units were non-Cossacks from the Astrakhan area, boosted by other non-Urals forces. At some stage there was a "Russian-Serbian" infantry unit, which may have supplied the core for the 2nd Plastoon Regiment above.
9th Urals Cossack Regiment
This regiment was operating around Guriev for most of this period, protecting it from attack from Turkestan (by land or sea). It is possible that the regiment is listed above by a territorial name.
13th Orenburg Cossack Regiment
This unit is well attested as fighting alongside the Urals Host for most of the war, probably in the region of Iletsk since that puts it closest to Orenburg.
The Urals Host seems to have had built up a force of several armoured cars.
At least one armoured train operated with the army, probably improvised.
The 9th Air Squadron had been able to supply occasional reconnaissance from mid-1918 in the Urals area initially. In July 1919 the AFSR sent the 10th Squadron to assist. These two squadrons flew along the Urals River front until the end of the war.
In March 1919 the British 266th Squadron arrived with their sea-planes to patrol the sea. In July with the British withdrawal they passed to Cossack control. The planes continued to patrol against Soviet naval attack, but also supported the attack along the coast towards Astrakhan of the Urals-Astrakhan Corps.
The Training Regiments were always the best units of the army, and were based on young recruits. They were kept intact when the 1919 reformation took place.
The 2nd Partisan and Pozdnaykov Regiments were reformed around a base of officers, volunteers, Cossacks from other hosts and peasants. They were also very good quality.
The Cossack regiment listed above were all restructured in March-April 1919 to be based around groups of villages. The 8th and 16th Regiments were left as conscious reformations of the old Imperial formations.
The Foot regiments were possibly largely non-Cossack in composition.
Small partisan detachments appear to have come and gone in addition to those listed above in the formal line-up. For example, a "Brykovski Partisan Detachment" appears in the 1st Division for a while.