Do I have to play a Dead of Winter event card as soon as I draw it, or can I choose to play it later?
You decide when (or if) to play any card from the item deck, including Event cards that add survivors. Players may play item cards (including event cards) on their turn, but they are not required to do so.

The one difference with Event cards is that they are not added to the waste pile but are instead removed from game.

Unfortunately the rulebook doesn't do a good job explaining Event cards, but this topic has come up repeatedly on the BGG rules forum. One such link posted below where one of the co-designers Jonathan Gilmour comments on a thread specific to this rule. 

http://boardgamegeek.com/article/17160807#17160807