On December 10th, 1920, U.S. President Woodrow Wilson was awarded the 1919 Nobel Peace Prize, in recognition of his effort to create The League of Nations. This was a rare late award, permitted under the rules but not previously done. The reason for the delay was that some of the committee were reluctant because the U.S. Senate had failed to ratify the Treaty of Versailles in November, 1919.
Growing up in a university town, I was familiar with the Nobel Prize; one of my friends was the youngest son of James B. Sumner (1887–1955), recipient in Chemistry for 1946, and his prize was on display in the family living room.
Sumner didn’t serve in WW1 since he was missing part of his left arm, but there were other Nobelists who did. I recently came across the interesting story of Robert Bárány (1876-1936), the 1914 recipient in Medicine, who was a doctor in the Austro-Hungarian Army. You can read this article at this address: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4325576/
I haven’t researched the subject in depth as it would require reading the official Nobel biographies of several hundred persons. But from my other research I can offer this partial list of others prize winners who are connected to the Great War:
Marie Curie née Sklowdowska (1867-1934) 1903 Physics 1911 Chemistry
Alexis Carrel (1873-1944) 1912 Medicine
Laurence Bragg (1890-1971) 1915 Physics
Fritz Haber (1868-1934) 1918 Chemistry
Frederic Banting (1891-1941) 1923 Medicine
Charles Dawes (1865-1951) 1925 Peace
Carl Bosch (1874–1940) 1931 Chemistry
Irène Joliot-Curie (1897-1956) 1935 Chemistry
Francis Peyton Rous (1879-1970) 1966 Medicine
F. A. Hayek (1899-1992) 1974 Economics
I should mention that during the five year period 1914 – 1918, 13 out of 25 Nobel prizes weren’t awarded, and the 1917 Peace prize was awarded to The Red Cross.