This article lists all the numerous means by which Mexicans have attempted to illegally cross over the Southern border, whether to smuggle others, import illegal drugs or for their own gratification.
"Dope has been smuggled across our Mexican border by submarine - pulled under the Rio Grande in sealed cans. It has been flown over in airplanes, even dropped from kites. On one occasion it was found tied in horses' manes and tails. It is often concealed in automobiles, more often tied to dogs who are trained to swim the river with it at night..."
More on this topic can be read here...
Marijuana was becoming a problem in 1938, too.
Read about it here.
Read another article about immigration
Click here to read about the U.S. Border Patrol.