Indeed, the participation of the British in the war with the Bolsheviks in the East of Russia was reduced mainly to the protection of the railway and various cargoes. The exception was a small detachment of sailors who first created and used an armored train with naval guns, and then these guns were transferred to two river steamers. These sailors were directly involved in the battles with the Red Army. There was also one episode with the participation of a battalion of British troops in battles against Bolshevik irregulars on the Ussuri front for a short period (it was in the summer and, accordingly, the winter uniform was not used).
However, there is always the option of playing "what if"?

For the British contingent in the East of Russia, black fur coats were indeed made:
