During the Winter War, which lasted from 1939 to 1940, Palmstrøm was a volunteer on the Finnish side, fighting against the Soviet Union. He returned to Norway to find his country invaded by Germany on 9 April 1940, and Palmstrøm took part in the subsequent fighting. He soon fled to the United Kingdom, where he joined Norwegian Independent Company 1 ("Kompani Linge"). He trained with the company in 1941 and 1942, and participated in the Måløy Raid. From 1942 to 1945 he was a defender in the Norwegian military court in London. He held the rank of lieutenant colonel. From 1944 to 1946 he also headed the "Norwegian national office", an office tasked with registering people whom the Norwegian government-in-exile regarded as war criminals.