From the FAQ (pg. 25):
Can I trigger The Dreadfort (Dreadfort Betrayal 105) when I play a Bolton Refugee (Refugees of War 83) with a printed STR of 2, and have Winterfell Castle (Core 25) in play, which gives the Bolton Refugee +1 STR?
Qualifying characteristics of cards are checked at the time a Response effect is triggered. In this example, the Bolton character enters play and has its STR raised to 3 (by the constant effect on Winterfell Castle) when it enters play, which occurs before the Response effect is triggered. When the Response is triggered, the character’s STR is 3, and it has just been played, so you can use The Dreadfort to draw a card.