The funny thing is that neither Saxony nor Saxony-Anhalt would be interested in that horsey stuff.

The Saxon Steed is old, much older than those later/Eastern Saxonies, and there are lots of legends around it. Duke Widukind, later defeated by Charlemagne, is said to have had a black horse. Once he became Christian, Charlie gave him a white horse. Widukind is probably buried in Herford, North Rhine Westphalia ...
Brunswick (e.g. the duchy of Braunschweig-Lüneburg) used the horse in its CoA, Hannover (kingdom and later Prussian province) used it, Westphalia (duchy and later Prussian province) used it – you will know the Westfalen notgeld "coins" from the 1920s with the horse on each piece.

So the newly founded state of Lower Saxony (re-)introduced the Saxon steed in 1946. North Rhine Westphalia, also newly founded, combined the symbols of Rhineland (river), Westphalia (horse) and Lippe (rose). The two horses (NI, NW) can peacefully coexist, hehe. As I wrote, the tail style on your token suggests Lower Saxony (or then Brunswick/Hannover) rather than Westphalia, but would the token maker (Lauer, from Nuremberg) know about such subtle differences? And would they care?
What I do find a little strange is that the piece says "Spielmarken". That is the plural; I would have expected the singular "Spielmarke" here ...
Christian