Here's a situation that came up in a game last night. I was playing Bara and had a Narrow Sea and a River Row out with a 2 cost Sansa Stark in my hand. Now I can use the Narrow Sea to reduce her cost by 2. My question is this: Is the out-of-house gold penalty part of the cost and can it be reduced with River Row and I pay one gold or must I pay 2 gold?

If, during marshalling, you wish to play a character, location, or attachment that is affiliated with a different House, the gold cost to play that card is increased by 2. This is called the gold penalty, and it is the price that must be paid for playing characters that are not loyal to your House.

As I read that and River Row "Marshalling: Kneel River Row to reduce the cost of the next character you play this phase by 1" I would say you can and I paid 1 gold but I wasn't 100% sure so I want to check here.

Yes. Gold penalties are added into the total cost before things that reduce total cost (like River Row) are applied.

Thanks, and in the spirit of concise Q&A here's how I save it in my own faq:

[Q] Can I use a reducer on the out-of-house gold penalty?

[A] Yes, the out-of-house gold penalty is added into the total cost before things that reduce the cost are applied.