If I play an event before I play fear of winter does that count as the one card I can play from hand that turn

No. What took place before the plot's effect becomes active has no bearing.

Think of it this way: Let's say there is a card that says "Players cannot initiate more than one challenge this round." After you initiate two challenges, I play the card. The effect does not stop you from initiating one more challenge subject to the card's effect any more than it would undo one of the two challenges that are already complete.