The Battele of the Bulge was fought in December 1944 thru January 1945 in the dead of Winter in Belgium and Luxenbourg in the North of Europe. The scenes in the movie show no snow on the ground and the people are dressed for warm weather. Part of the planning for the offensive was that the weather would be poor and overcast so Allied Air Superiority could not be brought to bear.
While talking in the Jeep, Brubaker says he is with Headquarters COMPANY of a Cavalry unit. In 1944 Cavalry units were listed as TROOP not COMPANY. The only Company in a Cavalry Squadron (equivalent to a Battalion) was the supporting Light Tank Company. All other units including Headquarters & Service were listed as Troop.