The bulk of Early War horses (born and raised between 1927 and November 1938) would have been issued in Braun-matt (RAL 840 B2 No18). This is a nice medium-to-dark shade of brown.
From November 1938 onward the Heer started issuing horses in Dunkelbraun (RAL 840 B2 No45). This was a darker shade.
By mid-1943, some units were authorized to use the "Ambush Scheme" coloring. Those units were receiving horses in Rotbraun (RAL 817). This was an even darker shade of brown, often referred to as "Schokoladenbraun" or "Chocolate Brown. Individual units were still being allowed to apply highlights to mane and tail in the field where appropriate.
Due to coloring pigment shortages, by October 1944 many units were receiving Rotbraun (RAL 812). This was a ligher shade of brown that RAL 817, requiring less pigments. Also, by this stage of the war units were no longer authorized to apply highlights to manes or tails.
These are, of course, the coloring regulations of horses issued from the factories. Units could, and often did, rely on locally sourced equines to replace campaign losses, so it would not be considered unusual if you wanted to spice up your horse color selections with other schemes. In fact, white horses on the Eastern Front during winter months were a highly prized possession. They required no additional upkeep, unlike regular colored horses which needed constant re-application of whitewash.
Hope this helps :-)
