It is highly unlikely that Germans, British or Americans would be out in winter weather without appropriate clothing, like gloves, to protect themselves from frostbite.
The jeep that Fleming is riding in during episode four has the bumper markings indicating it belongs to the 504 PIR, 82d Airborne Division. Most likely borrowed from a re-enactor, but the 82d was never in this area of Germany. Plus, these vehicles had side coverings to protect from winter weather, especially the wind, and these are missing.
The story is still in the 1940's but in the soundtrack one can hear "Aquellos Ojos Verdes", recorded in Rio de Janeiro, at the Odeon-EMI studios, in 1959.