What is the term used for the winter following john smith’s departure from jamestown?

The starving time.

Explanation:

Starving Time was the term assigned to the period of starvation that Jamestown, in the Colony of Virginia, went through during the winter of 1609–1610.  

Due to the lack of food, a collapsed leadership, and an assault by Powhatan Indian fighters, of the 500 inhabitants, only 60 residents remained alive by the time the spring came.

the united states broke it's neutrality was the constant german sinking of trading vessels resulting in the loss of lives, one example would be the lusitania.