Regarding cards that reduce costs for a specific house (for example, Godswood), they use icons to describe what cards receive the discount. I am a little unclear on exactly what cards are defined by theses icons.

Do they directly equate to the House shields, or are they referring to something else?

(To continue the example, would Godswood grant it's discount to Bran Stark AND Jon Snow, or just to Bran? Something I am missing entirely?)

Thanks!

Godswood will reduce the cost to play any character that has the Stark House affiliation. The little wolf-head symbol should be read as "Stark."

Neutral characters (the blank shield) do not have any House affiliation and cannot be reduced with those effects.

Just to link up ktom's answer with your question..."house affiliation" is denoted by the "house shields" which you referred to and which are located in the upper right hand corner of the card. (By the way, the cost of the Jon Snow in the Core Set can not be reduced by the Godswood, but there is a new version of Jon Snow in the "A Sword in the Darkness" chapter pack which has the Stark house affiliation).