wasn't this the period when the Wehrmacht was trying hard to motorise?
I don't think so. Motorcycles were probably the only motor vehicle which the Heer had in quantity during 1939.
The 4WD (i.e. military) version of the Opel Blitz 3 ton cargo truck entered mass production during July 1940.
The Sd.Kfz.251 medium half track had just entered production. The few early production vehicles were assigned to 1st Panzer Division during 1939.
The smaller Sd.Kfz.250 half track didn't enter service until 1941.
Most armored cars consisted of the small Sd.Kfz.231 which was built on a modified truck chassis.
German artillery towing tractors began entering service during the late 1930s but numbers were small. In fact most Heer field artillery remained horse drawn throughout the war.