The story regarding the origin of the phrase about a smoking snake is controversial. Due to the Brazilian dictatorship's unwillingness to get more deeply involved in the Allied war effort, by 1942 a popular saying was that "it's more likely for snakes to start to smoke now than for the BEF to set out." ("Mais fácil uma cobra fumar do que a FEB embarcar"). Until the BEF entered combat, the expression "a cobra vai fumar" ("snakes will smoke") was often used in Brazil in a context similar to "when pigs fly." As a result, the soldiers of the BEF called themselves
Cobras Fumantes (literally, Smoking Snakes), hence the divisional shoulder patch that showed a snake smoking a pipe. After the war the meaning was reversed, signifying that something will definitively happen and in a furious and aggressive way.
This fighting spirit is clearly illustrated by an episode that ocurred near the end of war. During the capture of Montese, three Brazilian soldiers, Arlindo Lúcio da Silva, Geraldo Baeta da Cruz, and Geraldo Rodrigues de Souza, when on a patrol, ran into an entire German Company. Though ordered to surrender, the Brazilians refused and fought to the death. In recognition of their bravery, the Germans would bury them and write on their crosses "Drei brasilianische Helden" (Three Brazilian Heroes). It is also interesting to note that the Brazilian Army was not racial-segregated, which caused some amusement to the Americans from the 5th Army.
For those interested the learn more about the Brazilian Expeditionary Force, I highly recommend the essay "Brazil and World War II: The Forgotten Ally" by Frank D. McCann (New Hapshire University):
http://www.tau.ac.il/eial/VI_2/mccann.htm
Douglas