Have had a chance to think about your request for information. As stated elsewhere Steve and I are attempting to construct an outline framework of units (and locations) in the early days of BAOR.
We have a certain amount of information on the Bad Harzburg/Goslar area which may be of interest to you. The American Army captured the towns in the last days of World War 2 and remained there throughout the Summer of 1945 before handing over military responsibilities to the British Army in July/August.
Units of 13 Infantry Brigade of 5 Infantry Brigade were the first British troops to be based in the area with their Headquarters in Goslar. However I think it most unlikely that your mother as a member of the ATS (future WRAC) would have been directly employed by or accommodated with these units.
More likely she would have worked for either the Control Commission Germany who were responsible for all civilian administrative matters including the police following the destruction of the Nazi dominated centralised system of government and the creation of a new democratic local system. Alternatively she could have worked for the newly created British Frontier Service who were responsible for the control of all civilian movement across the borders of the British and Soviet Zones of Occupation ( Bad Harzburg was on the actual border and Goslar was to become a very important Sector Headquarters).
The photographs might provide proof of my theory as both organisations wore military style uniforms in the early days of BAOR, CCG Army style, BFS Naval style. A small shoulder flash would indicate their specialist roles.. Unfortunately to date we have no details of exact locations but Schloss were a popular site throughout the British Zone particularly if previously used by Nazi authorities or prominent Hitler supporters.
Your comments regarding horses are extremely relevant. Not withstanding the reputation of the German Panzer (Armoured Division) much of the Wehrmacht relied on horses to provide horses to provide a vital part of their resupply systems. At the end of World War 2 the British Army cheerfully signed on a significant number for recreation purposes. I have also seen a brief reference that horses were also used in the hilly, woody countryside of the Harz mountains to increase the mobility of the military Patrols along the border between the two zones in the early days of BAOR designed to stop the illegal movement of people and more importantly black market smuggling activities across the border.