Should you address the woman or man first?

Whoever you want to, because if you always address a man first, that is discrimination. Although we agree all people are equal, it is respectful to address the senior person present first, man or woman. If you are writing a letter to a couple, conventionally the man is considered the head of the house. Many prioritize in favour of the one they require action from. It is, however, your choice. Just remember to do it with respect for the people and not blindly in the pursuit of a misguided sense of political correctness, for that would be discrimination.