Hair becoming white in one night after tremendous stress
The physiological condition you are looking for is commonly called Marie Antoinette Syndrome. 

Under extreme psychological stress, the hair of the person does turn white but not in a single night (takes place slowly over successive days; in a matter of weeks) and cases of this has been reported worldwide generally in warzones.

Contrary to what you suggest, this phenomenon is extremely rare and I doubt many soldiers experience it.

Source- http://archderm.jamanetwork.com/mobile/article.aspx?articleid=712060

Another interesting tidbit the author mentions is whether Marie Antoinette herself suffered from it or not. The author goes in depth on the topic; regardless the syndrome is definitely real with documented cases. It is also known as canities subita. 

Most in the scientific field now refer to it as an acute episode of diffuse alopecia areata. Alopecia areata is patchy hair-loss. This syndrome is referred to as such because the white hair eventually fall off.